LMFDB - Embedded newform 275.2.y.b.34.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [275,2,Mod(34,275)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(275, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([7, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("275.34");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 275 = 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	275.y (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.19588605559$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			34.14
Character	$\chi$	$=$	275.34
Dual form			275.2.y.b.89.14

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.59706 - 2.19817i) q^{2} +(0.774067 - 0.251509i) q^{3} +(-1.66330 - 5.11912i) q^{4} +(1.70943 + 1.44147i) q^{5} +(0.683373 - 2.10321i) q^{6} +0.417733i q^{7} +(-8.74087 - 2.84008i) q^{8} +(-1.89113 + 1.37399i) q^{9} +(5.89867 - 1.45551i) q^{10} +(0.809017 + 0.587785i) q^{11} +(-2.57501 - 3.54420i) q^{12} +(-1.70490 - 2.34659i) q^{13} +(0.918248 + 0.667146i) q^{14} +(1.68576 + 0.685855i) q^{15} +(-11.4935 + 8.35055i) q^{16} +(6.50132 + 2.11241i) q^{17} +6.35136i q^{18} +(0.0183461 - 0.0564634i) q^{19} +(4.53575 - 11.1484i) q^{20} +(0.105064 + 0.323353i) q^{21} +(2.58410 - 0.839626i) q^{22} +(-4.73883 + 6.52244i) q^{23} -7.48033 q^{24} +(0.844328 + 4.92820i) q^{25} -7.88104 q^{26} +(-2.55349 + 3.51457i) q^{27} +(2.13842 - 0.694816i) q^{28} +(-0.839822 - 2.58471i) q^{29} +(4.19989 - 2.61023i) q^{30} +(1.68388 - 5.18245i) q^{31} +20.2197i q^{32} +(0.774067 + 0.251509i) q^{33} +(15.0265 - 10.9174i) q^{34} +(-0.602150 + 0.714087i) q^{35} +(10.1791 + 7.39556i) q^{36} +(-4.82073 - 6.63516i) q^{37} +(-0.0948162 - 0.130503i) q^{38} +(-1.90990 - 1.38762i) q^{39} +(-10.8481 - 17.4546i) q^{40} +(-0.829485 + 0.602656i) q^{41} +(0.878579 + 0.285468i) q^{42} +1.25198i q^{43} +(1.66330 - 5.11912i) q^{44} +(-5.21332 - 0.377268i) q^{45} +(6.76921 + 20.8335i) q^{46} +(4.18899 - 1.36108i) q^{47} +(-6.79653 + 9.35462i) q^{48} +6.82550 q^{49} +(12.1815 + 6.01466i) q^{50} +5.56375 q^{51} +(-9.17672 + 12.6307i) q^{52} +(3.17803 - 1.03261i) q^{53} +(3.64755 + 11.2260i) q^{54} +(0.535686 + 2.17095i) q^{55} +(1.18640 - 3.65135i) q^{56} -0.0483206i q^{57} +(-7.02287 - 2.28187i) q^{58} +(-5.62783 + 4.08886i) q^{59} +(0.707046 - 9.77038i) q^{60} +(0.616446 + 0.447874i) q^{61} +(-8.70263 - 11.9781i) q^{62} +(-0.573959 - 0.789987i) q^{63} +(21.4593 + 15.5911i) q^{64} +(0.468130 - 6.46890i) q^{65} +(1.78909 - 1.29985i) q^{66} +(-6.35746 - 2.06566i) q^{67} -36.7946i q^{68} +(-2.02772 + 6.24067i) q^{69} +(0.608013 + 2.46407i) q^{70} +(-4.01481 - 12.3563i) q^{71} +(20.4323 - 6.63887i) q^{72} +(3.39913 - 4.67850i) q^{73} -22.2842 q^{74} +(1.89305 + 3.60240i) q^{75} -0.319558 q^{76} +(-0.245537 + 0.337953i) q^{77} +(-6.10045 + 1.98216i) q^{78} +(3.78211 + 11.6401i) q^{79} +(-31.6845 - 2.29289i) q^{80} +(1.07442 - 3.30672i) q^{81} +2.78583i q^{82} +(-14.6506 - 4.76028i) q^{83} +(1.48053 - 1.07567i) q^{84} +(8.06861 + 12.9825i) q^{85} +(2.75207 + 1.99950i) q^{86} +(-1.30016 - 1.78951i) q^{87} +(-5.40216 - 7.43543i) q^{88} +(3.53639 + 2.56934i) q^{89} +(-9.15530 + 10.8572i) q^{90} +(0.980249 - 0.712193i) q^{91} +(41.2712 + 13.4098i) q^{92} -4.43507i q^{93} +(3.69818 - 11.3818i) q^{94} +(0.112752 - 0.0700751i) q^{95} +(5.08545 + 15.6514i) q^{96} +(-17.9371 + 5.82813i) q^{97} +(10.9008 - 15.0036i) q^{98} -2.33756 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 16 q^{4} - 7 q^{5} - 4 q^{6} - 15 q^{8} + 10 q^{9} + 10 q^{10} + 14 q^{11} - 20 q^{12} - 6 q^{14} - 21 q^{15} - 20 q^{16} + 20 q^{17} + 10 q^{19} + 22 q^{20} - 6 q^{21} + 10 q^{23} - 62 q^{24} + 9 q^{25}+ \cdots + 70 q^{99}+O(q^{100}) $ 56 * q + 16 * q^4 - 7 * q^5 - 4 * q^6 - 15 * q^8 + 10 * q^9 + 10 * q^10 + 14 * q^11 - 20 * q^12 - 6 * q^14 - 21 * q^15 - 20 * q^16 + 20 * q^17 + 10 * q^19 + 22 * q^20 - 6 * q^21 + 10 * q^23 - 62 * q^24 + 9 * q^25 - 4 * q^26 + 18 * q^29 - 129 * q^30 - 16 * q^34 + 42 * q^35 - 26 * q^36 - 65 * q^37 - 20 * q^38 + 20 * q^39 - 28 * q^40 - 10 * q^41 + 60 * q^42 - 16 * q^44 - 18 * q^45 + 6 * q^46 - 25 * q^47 + 15 * q^48 - 104 * q^49 + 98 * q^50 + 54 * q^51 + 90 * q^52 + 5 * q^53 + 55 * q^54 - 3 * q^55 + 10 * q^56 - 10 * q^58 + 34 * q^59 + 133 * q^60 - 20 * q^61 - 10 * q^62 + 20 * q^63 + 25 * q^64 - 10 * q^65 + 4 * q^66 - 15 * q^67 - 2 * q^69 - 4 * q^70 - 13 * q^71 - 5 * q^72 - 70 * q^73 - 30 * q^74 - 80 * q^75 + 140 * q^76 - 65 * q^78 + 15 * q^79 - 131 * q^80 - 99 * q^81 + 60 * q^83 + 76 * q^84 + 43 * q^85 + 43 * q^86 - 175 * q^87 + 30 * q^88 + 27 * q^89 + 73 * q^90 - 10 * q^91 - 80 * q^92 - 17 * q^94 + 18 * q^95 - 148 * q^96 - 15 * q^97 - 80 * q^98 + 70 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/275\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$1$	$e\left(\frac{7}{10}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.59706	−	2.19817i	1.12929	−	1.55434i	0.339891	−	0.940465i	$-0.389610\pi$
$2$	1.59706	−	2.19817i	1.12929	−	1.55434i	0.789403	−	0.613875i	$-0.210390\pi$
$3$	0.774067	−	0.251509i	0.446908	−	0.145209i	−0.0769128	−	0.997038i	$-0.524506\pi$
$3$	0.774067	−	0.251509i	0.446908	−	0.145209i	0.523820	+	0.851829i	$0.324506\pi$
$4$	−1.66330	−	5.11912i	−0.831651	−	2.55956i
$5$	1.70943	+	1.44147i	0.764482	+	0.644645i
$5$	1.70943	+	1.44147i	0.764482	+	0.644645i
$6$	0.683373	−	2.10321i	0.278986	−	0.858630i
$7$			0.417733i			0.157888i	0.996879	+	0.0789441i	$0.0251549\pi$
$7$			0.417733i			0.157888i	−0.996879	+	0.0789441i	$0.974845\pi$
$8$	−8.74087	−	2.84008i	−3.09037	−	1.00412i
$9$	−1.89113	+	1.37399i	−0.630376	+	0.457995i
$10$	5.89867	−	1.45551i	1.86532	−	0.460271i
$11$	0.809017	+	0.587785i	0.243928	+	0.177224i
$11$	0.809017	+	0.587785i	0.243928	+	0.177224i
$12$	−2.57501	−	3.54420i	−0.743342	−	1.02312i
$13$	−1.70490	−	2.34659i	−0.472854	−	0.650828i	0.504258	−	0.863553i	$-0.331766\pi$
$13$	−1.70490	−	2.34659i	−0.472854	−	0.650828i	−0.977112	+	0.212725i	$0.931766\pi$
$14$	0.918248	+	0.667146i	0.245412	+	0.178302i
$15$	1.68576	+	0.685855i	0.435261	+	0.177087i
$16$	−11.4935	+	8.35055i	−2.87339	+	2.08764i
$17$	6.50132	+	2.11241i	1.57680	+	0.512334i	0.961230	−	0.275746i	$-0.0889250\pi$
$17$	6.50132	+	2.11241i	1.57680	+	0.512334i	0.615572	+	0.788081i	$0.288925\pi$
$18$			6.35136i			1.49703i
$19$	0.0183461	−	0.0564634i	0.00420888	−	0.0129536i	−0.948930	−	0.315487i	$-0.897832\pi$
$19$	0.0183461	−	0.0564634i	0.00420888	−	0.0129536i	0.953139	+	0.302533i	$0.0978323\pi$
$20$	4.53575	−	11.1484i	1.01422	−	2.49286i
$21$	0.105064	+	0.323353i	0.0229268	+	0.0705615i
$22$	2.58410	−	0.839626i	0.550932	−	0.179009i
$23$	−4.73883	+	6.52244i	−0.988115	+	1.36002i	−0.0557733	+	0.998443i	$0.517762\pi$
$23$	−4.73883	+	6.52244i	−0.988115	+	1.36002i	−0.932341	+	0.361580i	$0.882238\pi$
$24$	−7.48033			−1.52692
$25$	0.844328	+	4.92820i	0.168866	+	0.985639i
$26$	−7.88104			−1.54560
$27$	−2.55349	+	3.51457i	−0.491419	+	0.676380i
$28$	2.13842	−	0.694816i	0.404124	−	0.131308i
$29$	−0.839822	−	2.58471i	−0.155951	−	0.479968i	0.842305	−	0.539001i	$-0.181198\pi$
$29$	−0.839822	−	2.58471i	−0.155951	−	0.479968i	−0.998256	+	0.0590332i	$0.981198\pi$
$30$	4.19989	−	2.61023i	0.766791	−	0.476560i
$31$	1.68388	−	5.18245i	0.302434	−	0.930795i	−0.678189	−	0.734888i	$-0.737235\pi$
$31$	1.68388	−	5.18245i	0.302434	−	0.930795i	0.980622	−	0.195907i	$-0.0627652\pi$
$32$			20.2197i			3.57437i
$33$	0.774067	+	0.251509i	0.134748	+	0.0437822i
$34$	15.0265	−	10.9174i	2.57702	−	1.87231i
$35$	−0.602150	+	0.714087i	−0.101782	+	0.120703i
$36$	10.1791	+	7.39556i	1.69652	+	1.23259i
$37$	−4.82073	−	6.63516i	−0.792523	−	1.09081i	−0.993789	−	0.111277i	$-0.964506\pi$
$37$	−4.82073	−	6.63516i	−0.792523	−	1.09081i	0.201267	−	0.979536i	$-0.435494\pi$
$38$	−0.0948162	−	0.130503i	−0.0153812	−	0.0211704i
$39$	−1.90990	−	1.38762i	−0.305828	−	0.222197i
$40$	−10.8481	−	17.4546i	−1.71523	−	2.75982i
$41$	−0.829485	+	0.602656i	−0.129544	+	0.0941190i	−0.650670	−	0.759360i	$-0.725512\pi$
$41$	−0.829485	+	0.602656i	−0.129544	+	0.0941190i	0.521127	+	0.853479i	$0.325512\pi$
$42$	0.878579	+	0.285468i	0.135568	+	0.0440486i
$43$			1.25198i			0.190926i	0.995433	+	0.0954628i	$0.0304331\pi$
$43$			1.25198i			0.190926i	−0.995433	+	0.0954628i	$0.969567\pi$
$44$	1.66330	−	5.11912i	0.250752	−	0.771736i
$45$	−5.21332	−	0.377268i	−0.777156	−	0.0562398i
$46$	6.76921	+	20.8335i	0.998066	+	3.07173i
$47$	4.18899	−	1.36108i	0.611026	−	0.198535i	0.0128744	−	0.999917i	$-0.495902\pi$
$47$	4.18899	−	1.36108i	0.611026	−	0.198535i	0.598152	+	0.801383i	$0.295902\pi$
$48$	−6.79653	+	9.35462i	−0.980994	+	1.35022i
$49$	6.82550			0.975071
$50$	12.1815	+	6.01466i	1.72272	+	0.850602i
$51$	5.56375			0.779081
$52$	−9.17672	+	12.6307i	−1.27258	+	1.75156i
$53$	3.17803	−	1.03261i	0.436536	−	0.141839i	−0.0825007	−	0.996591i	$-0.526291\pi$
$53$	3.17803	−	1.03261i	0.436536	−	0.141839i	0.519037	+	0.854752i	$0.326291\pi$
$54$	3.64755	+	11.2260i	0.496368	+	1.52766i
$55$	0.535686	+	2.17095i	0.0722319	+	0.292731i
$56$	1.18640	−	3.65135i	0.158539	−	0.487932i
$57$		−	0.0483206i		−	0.00640022i
$58$	−7.02287	−	2.28187i	−0.922148	−	0.299624i
$59$	−5.62783	+	4.08886i	−0.732682	+	0.532324i	−0.890411	−	0.455158i	$-0.849583\pi$
$59$	−5.62783	+	4.08886i	−0.732682	+	0.532324i	0.157729	+	0.987482i	$0.449583\pi$
$60$	0.707046	−	9.77038i	0.0912792	−	1.26135i
$61$	0.616446	+	0.447874i	0.0789278	+	0.0573444i	0.626549	−	0.779382i	$-0.284467\pi$
$61$	0.616446	+	0.447874i	0.0789278	+	0.0573444i	−0.547622	+	0.836726i	$0.684467\pi$
$62$	−8.70263	−	11.9781i	−1.10524	−	1.52123i
$63$	−0.573959	−	0.789987i	−0.0723121	−	0.0995290i
$64$	21.4593	+	15.5911i	2.68241	+	1.94888i
$65$	0.468130	−	6.46890i	0.0580644	−	0.802369i
$66$	1.78909	−	1.29985i	0.220222	−	0.160001i
$67$	−6.35746	−	2.06566i	−0.776687	−	0.252361i	−0.106262	−	0.994338i	$-0.533888\pi$
$67$	−6.35746	−	2.06566i	−0.776687	−	0.252361i	−0.670425	+	0.741977i	$0.733888\pi$
$68$		−	36.7946i		−	4.46200i
$69$	−2.02772	+	6.24067i	−0.244108	+	0.751288i
$70$	0.608013	+	2.46407i	0.0726714	+	0.294513i
$71$	−4.01481	−	12.3563i	−0.476471	−	1.46643i	−0.843964	−	0.536400i	$-0.819784\pi$
$71$	−4.01481	−	12.3563i	−0.476471	−	1.46643i	0.367493	−	0.930026i	$-0.380216\pi$
$72$	20.4323	−	6.63887i	2.40798	−	0.782399i
$73$	3.39913	−	4.67850i	0.397838	−	0.547577i	−0.562362	−	0.826891i	$-0.690107\pi$
$73$	3.39913	−	4.67850i	0.397838	−	0.547577i	0.960200	+	0.279314i	$0.0901071\pi$
$74$	−22.2842			−2.59049
$75$	1.89305	+	3.60240i	0.218591	+	0.415969i
$76$	−0.319558			−0.0366558
$77$	−0.245537	+	0.337953i	−0.0279816	+	0.0385133i
$78$	−6.10045	+	1.98216i	−0.690740	+	0.224435i
$79$	3.78211	+	11.6401i	0.425521	+	1.30962i	0.902495	+	0.430701i	$0.141734\pi$
$79$	3.78211	+	11.6401i	0.425521	+	1.30962i	−0.476974	+	0.878917i	$0.658266\pi$
$80$	−31.6845	−	2.29289i	−3.54244	−	0.256353i
$81$	1.07442	−	3.30672i	0.119380	−	0.367414i
$82$			2.78583i			0.307643i
$83$	−14.6506	−	4.76028i	−1.60812	−	0.522509i	−0.639020	−	0.769190i	$-0.720660\pi$
$83$	−14.6506	−	4.76028i	−1.60812	−	0.522509i	−0.969097	+	0.246682i	$0.920660\pi$
$84$	1.48053	−	1.07567i	0.161539	−	0.117365i
$85$	8.06861	+	12.9825i	0.875164	+	1.40815i
$86$	2.75207	+	1.99950i	0.296763	+	0.215611i
$87$	−1.30016	−	1.78951i	−0.139391	−	0.191856i
$88$	−5.40216	−	7.43543i	−0.575872	−	0.792620i
$89$	3.53639	+	2.56934i	0.374856	+	0.272349i	0.759222	−	0.650832i	$-0.225580\pi$
$89$	3.53639	+	2.56934i	0.374856	+	0.272349i	−0.384365	+	0.923181i	$0.625580\pi$
$90$	−9.15530	+	10.8572i	−0.965053	+	1.14445i
$91$	0.980249	−	0.712193i	0.102758	−	0.0746581i
$92$	41.2712	+	13.4098i	4.30282	+	1.39807i
$93$		−	4.43507i		−	0.459896i
$94$	3.69818	−	11.3818i	0.381438	−	1.17395i
$95$	0.112752	−	0.0700751i	0.0115681	−	0.00718955i
$96$	5.08545	+	15.6514i	0.519032	+	1.59741i
$97$	−17.9371	+	5.82813i	−1.82124	+	0.591757i	−0.821471	+	0.570251i	$0.806846\pi$
$97$	−17.9371	+	5.82813i	−1.82124	+	0.591757i	−0.999769	+	0.0215058i	$0.993154\pi$
$98$	10.9008	−	15.0036i	1.10114	−	1.51559i
$99$	−2.33756			−0.234934
$100$	23.8236	−	12.5193i	2.38236	−	1.25193i
$101$	18.0879			1.79982			0.899909	−	0.436078i	$-0.143633\pi$
$101$	18.0879			1.79982			0.899909	+	0.436078i	$0.143633\pi$
$102$	8.88566	−	12.2301i	0.879811	−	1.21096i
$103$	−11.8462	+	3.84906i	−1.16724	+	0.379260i	−0.827612	−	0.561300i	$-0.810301\pi$
$103$	−11.8462	+	3.84906i	−1.16724	+	0.379260i	−0.339629	+	0.940560i	$0.610301\pi$
$104$	8.23779	+	25.3533i	0.807782	+	2.48610i
$105$	−0.286504	+	0.704197i	−0.0279600	+	0.0687226i
$106$	2.80568	−	8.63499i	0.272512	−	0.838704i
$107$		−	4.97733i		−	0.481177i	−0.970627	−	0.240588i	$-0.922660\pi$
$107$		−	4.97733i		−	0.481177i	0.970627	−	0.240588i	$-0.0773404\pi$
$108$	22.2387	+	7.22580i	2.13992	+	0.695303i
$109$	−5.96820	+	4.33615i	−0.571650	+	0.415328i	−0.835704	−	0.549180i	$-0.814940\pi$
$109$	−5.96820	+	4.33615i	−0.571650	+	0.415328i	0.264054	+	0.964508i	$0.414940\pi$
$110$	5.62765	+	2.28962i	0.536575	+	0.218307i
$111$	−5.40037	−	3.92360i	−0.512580	−	0.372411i
$112$	−3.48830	−	4.80124i	−0.329614	−	0.453674i
$113$	3.27792	+	4.51166i	0.308360	+	0.424422i	0.934869	−	0.354993i	$-0.115517\pi$
$113$	3.27792	+	4.51166i	0.308360	+	0.424422i	−0.626509	+	0.779414i	$0.715517\pi$
$114$	−0.106217	−	0.0771711i	−0.00994812	−	0.00722773i
$115$	−17.5026	+	4.31880i	−1.63213	+	0.402730i
$116$	−11.8345	+	8.59829i	−1.09881	+	0.798332i
$117$	6.44837	+	2.09520i	0.596152	+	0.193701i
$118$			18.9011i			1.73999i
$119$	−0.882423	+	2.71582i	−0.0808916	+	0.248959i
$120$	−12.7871	−	10.7827i	−1.16730	−	0.984318i
$121$	0.309017	+	0.951057i	0.0280925	+	0.0864597i
$122$	1.96901	−	0.639769i	0.178265	−	0.0579219i
$123$	−0.490503	+	0.675119i	−0.0442271	+	0.0608734i
$124$	−29.3304			−2.63394
$125$	−5.66052	+	9.64150i	−0.506293	+	0.862362i
$126$	−2.65317			−0.236364
$127$	5.92807	−	8.15928i	0.526031	−	0.724019i	−0.460488	−	0.887666i	$-0.652326\pi$
$127$	5.92807	−	8.15928i	0.526031	−	0.724019i	0.986519	+	0.163646i	$0.0523256\pi$
$128$	30.0834	−	9.77468i	2.65902	−	0.863968i
$129$	0.314886	+	0.969118i	0.0277241	+	0.0853261i
$130$	−13.4721	−	11.3603i	−1.18158	−	0.996362i
$131$	−1.00874	+	3.10460i	−0.0881344	+	0.271250i	−0.985404	−	0.170234i	$-0.945548\pi$
$131$	−1.00874	+	3.10460i	−0.0881344	+	0.271250i	0.897269	+	0.441484i	$0.145548\pi$
$132$		−	4.38087i		−	0.381306i
$133$	0.0235866	+	0.00766376i	0.00204522	+	0.000664532i
$134$	−14.6939	+	10.6758i	−1.26936	+	0.922246i
$135$	−9.43117	+	2.32716i	−0.811706	+	0.200290i
$136$	−50.8278	−	36.9286i	−4.35845	−	3.16660i
$137$	−5.11528	−	7.04058i	−0.437028	−	0.601517i	0.532521	−	0.846417i	$-0.321245\pi$
$137$	−5.11528	−	7.04058i	−0.437028	−	0.601517i	−0.969548	+	0.244900i	$0.921245\pi$
$138$	10.4796	+	14.4240i	0.892087	+	1.22785i
$139$	4.60896	+	3.34861i	0.390927	+	0.284025i	0.765835	−	0.643037i	$-0.222326\pi$
$139$	4.60896	+	3.34861i	0.390927	+	0.284025i	−0.374908	+	0.927062i	$0.622326\pi$
$140$	4.65705	+	1.89473i	0.393593	+	0.160134i
$141$	2.90023	−	2.10714i	0.244243	−	0.177453i
$142$	−33.5732	−	10.9086i	−2.81740	−	0.915429i
$143$		−	2.90055i		−	0.242556i
$144$	10.2622	−	31.5839i	0.855187	−	2.63199i
$145$	2.29016	−	5.62896i	0.190187	−	0.467460i
$146$	−4.85551	−	14.9437i	−0.401845	−	1.23675i
$147$	5.28339	−	1.71668i	0.435767	−	0.141589i
$148$	−25.9478	+	35.7141i	−2.13290	+	2.93568i
$149$	4.13669			0.338891			0.169446	−	0.985540i	$-0.445802\pi$
$149$	4.13669			0.338891			0.169446	+	0.985540i	$0.445802\pi$
$150$	10.9420	+	1.59200i	0.893411	+	0.129986i
$151$	6.60457			0.537472			0.268736	−	0.963214i	$-0.413394\pi$
$151$	6.60457			0.537472			0.268736	+	0.963214i	$0.413394\pi$
$152$	−0.320721	+	0.441435i	−0.0260139	+	0.0358051i
$153$	−15.1973	+	4.93789i	−1.22863	+	0.399205i
$154$	0.350740	+	1.07947i	0.0282634	+	0.0869858i
$155$	10.3488	−	6.43179i	0.831238	−	0.516614i
$156$	−3.92666	+	12.0850i	−0.314384	+	0.967575i
$157$			4.49360i			0.358629i	0.983792	+	0.179314i	$0.0573879\pi$
$157$			4.49360i			0.358629i	−0.983792	+	0.179314i	$0.942612\pi$
$158$	31.6273	+	10.2763i	2.51613	+	0.817540i
$159$	2.20030	−	1.59861i	0.174495	−	0.126778i
$160$	−29.1461	+	34.5643i	−2.30420	+	2.73254i
$161$	−2.72464	−	1.97957i	−0.214732	−	0.156012i
$162$	−5.55282	−	7.64281i	−0.436271	−	0.600475i
$163$	−7.48093	−	10.2966i	−0.585952	−	0.806493i	0.408381	−	0.912812i	$-0.366094\pi$
$163$	−7.48093	−	10.2966i	−0.585952	−	0.806493i	−0.994332	+	0.106319i	$0.966094\pi$
$164$	4.46475	+	3.24383i	0.348638	+	0.253300i
$165$	0.960672	+	1.54573i	0.0747882	+	0.120335i
$166$	−33.8619	+	24.6021i	−2.62819	+	1.90949i
$167$	−0.134130	−	0.0435813i	−0.0103793	−	0.00337242i	0.303823	−	0.952729i	$-0.401737\pi$
$167$	−0.134130	−	0.0435813i	−0.0103793	−	0.00337242i	−0.314202	+	0.949356i	$0.601737\pi$
$168$		−	3.12478i		−	0.241082i
$169$	1.41741	−	4.36233i	0.109031	−	0.335564i
$170$	41.4238	+	2.99768i	3.17706	+	0.229912i
$171$	0.0428851	+	0.131987i	0.00327951	+	0.0100933i
$172$	6.40905	−	2.08243i	0.488685	−	0.158783i
$173$	10.2362	−	14.0889i	0.778244	−	1.07116i	−0.217229	−	0.976121i	$-0.569702\pi$
$173$	10.2362	−	14.0889i	0.778244	−	1.07116i	0.995473	−	0.0950409i	$-0.0302982\pi$
$174$	−6.01008			−0.455623
$175$	−2.05867	+	0.352704i	−0.155621	+	0.0266619i
$176$	−14.2068			−1.07088
$177$	−3.32793	+	4.58050i	−0.250143	+	0.344292i
$178$	11.2957	−	3.67019i	0.846646	−	0.275092i
$179$	0.559882	+	1.72314i	0.0418475	+	0.128793i	0.969798	−	0.243911i	$-0.0784305\pi$
$179$	0.559882	+	1.72314i	0.0418475	+	0.128793i	−0.927950	+	0.372705i	$0.878431\pi$
$180$	6.74004	+	27.3151i	0.502373	+	2.03595i
$181$	−1.80191	+	5.54570i	−0.133935	+	0.412209i	−0.995423	−	0.0955691i	$-0.969533\pi$
$181$	−1.80191	+	5.54570i	−0.133935	+	0.412209i	0.861488	+	0.507778i	$0.169533\pi$
$182$		−	3.29217i		−	0.244032i
$183$	0.589815	+	0.191642i	0.0436004	+	0.0141666i
$184$	59.9458	−	43.5532i	4.41926	−	3.21078i
$185$	1.32367	−	18.2913i	0.0973184	−	1.34480i
$186$	−9.74904	−	7.08309i	−0.714834	−	0.519357i
$187$	4.01804	+	5.53036i	0.293828	+	0.404420i
$188$	−13.9351	−	19.1800i	−1.01632	−	1.39885i
$189$	−1.46815	−	1.06668i	−0.106793	−	0.0775893i
$190$	0.0260346	−	0.359762i	0.00188875	−	0.0260998i
$191$	6.54557	−	4.75563i	0.473621	−	0.344105i	−0.325230	−	0.945635i	$-0.605442\pi$
$191$	6.54557	−	4.75563i	0.473621	−	0.344105i	0.798851	+	0.601529i	$0.205442\pi$
$192$	20.5322	+	6.67131i	1.48178	+	0.481461i
$193$			26.6326i			1.91706i	0.284995	+	0.958529i	$0.408008\pi$
$193$			26.6326i			1.91706i	−0.284995	+	0.958529i	$0.591992\pi$
$194$	−15.8355	+	48.7367i	−1.13692	+	3.49909i
$195$	−1.26463	−	5.12510i	−0.0905618	−	0.367016i
$196$	−11.3529	−	34.9405i	−0.810919	−	2.49575i
$197$	8.00771	−	2.60186i	0.570526	−	0.185375i	−0.00952600	−	0.999955i	$-0.503032\pi$
$197$	8.00771	−	2.60186i	0.570526	−	0.185375i	0.580052	+	0.814580i	$0.303032\pi$
$198$	−3.73324	+	5.13836i	−0.265310	+	0.365167i
$199$	−13.7023			−0.971329			−0.485664	−	0.874145i	$-0.661422\pi$
$199$	−13.7023			−0.971329			−0.485664	+	0.874145i	$0.661422\pi$
$200$	6.61631	−	45.4747i	0.467844	−	3.21555i
$201$	−5.44063			−0.383753
$202$	28.8876	−	39.7604i	2.03252	−	2.79753i
$203$	1.07972	−	0.350822i	0.0757813	−	0.0246228i
$204$	−9.25419	−	28.4815i	−0.647923	−	1.99410i
$205$	−2.28666	−	0.165477i	−0.159707	−	0.0115574i
$206$	−10.4582	+	32.1872i	−0.728660	+	2.24259i
$207$		−	18.8459i		−	1.30988i
$208$	39.1907	+	12.7338i	2.71738	+	0.882932i
$209$	0.0480306	−	0.0348963i	0.00332235	−	0.00241383i
$210$	1.09038	+	1.75443i	0.0752433	+	0.121067i
$211$	12.1095	+	8.79809i	0.833655	+	0.605685i	0.920591	−	0.390528i	$-0.127708\pi$
$211$	12.1095	+	8.79809i	0.833655	+	0.605685i	−0.0869364	+	0.996214i	$0.527708\pi$
$212$	−10.5721	−	14.5512i	−0.726092	−	0.999379i
$213$	−6.21547	−	8.55486i	−0.425877	−	0.586169i
$214$	−10.9410	−	7.94911i	−0.747912	−	0.543390i
$215$	−1.80470	+	2.14018i	−0.123079	+	0.145959i
$216$	32.3014	−	23.4683i	2.19783	−	1.59682i
$217$	2.16488	+	0.703412i	0.146962	+	0.0477507i
$218$			20.0442i			1.35757i
$219$	1.45447	−	4.47639i	0.0982837	−	0.302486i
$220$	10.2224	−	6.35319i	0.689191	−	0.428332i
$221$	−6.12714	−	18.8574i	−0.412156	−	1.26849i
$222$	−17.2495	+	5.60469i	−1.15771	+	0.376162i
$223$	7.35833	−	10.1279i	0.492750	−	0.678212i	−0.488142	−	0.872764i	$-0.662325\pi$
$223$	7.35833	−	10.1279i	0.492750	−	0.678212i	0.980892	+	0.194552i	$0.0623253\pi$
$224$	−8.44644			−0.564352
$225$	−8.36800	−	8.15976i	−0.557867	−	0.543984i
$226$	15.1524			1.00793
$227$	−3.63309	+	5.00052i	−0.241137	+	0.331896i	−0.912383	−	0.409338i	$-0.865760\pi$
$227$	−3.63309	+	5.00052i	−0.241137	+	0.331896i	0.671246	+	0.741235i	$0.265760\pi$
$228$	−0.247359	+	0.0803718i	−0.0163817	+	0.00532275i
$229$	3.63231	+	11.1791i	0.240030	+	0.738735i	0.996414	+	0.0846082i	$0.0269639\pi$
$229$	3.63231	+	11.1791i	0.240030	+	0.738735i	−0.756385	+	0.654127i	$0.773036\pi$
$230$	−18.4593	+	45.3711i	−1.21717	+	2.99168i
$231$	−0.105064	+	0.323353i	−0.00691269	+	0.0212751i
$232$			24.9778i			1.63987i
$233$	22.8518	+	7.42500i	1.49707	+	0.486428i	0.939162	−	0.343474i	$-0.111604\pi$
$233$	22.8518	+	7.42500i	1.49707	+	0.486428i	0.557909	+	0.829902i	$0.311604\pi$
$234$	14.9041	−	10.8284i	0.974309	−	0.707877i
$235$	9.12276	+	3.71162i	0.595103	+	0.242119i
$236$	30.2921	+	22.0085i	1.97185	+	1.43263i
$237$	5.85521	+	8.05901i	0.380337	+	0.523489i
$238$	4.56054	+	6.27705i	0.295616	+	0.406881i
$239$	6.06777	+	4.40849i	0.392491	+	0.285162i	0.766476	−	0.642273i	$-0.222009\pi$
$239$	6.06777	+	4.40849i	0.392491	+	0.285162i	−0.373984	+	0.927435i	$0.622009\pi$
$240$	−25.1026	+	6.19411i	−1.62037	+	0.399828i
$241$	19.3089	−	14.0288i	1.24380	−	0.903673i	0.245953	−	0.969282i	$-0.420899\pi$
$241$	19.3089	−	14.0288i	1.24380	−	0.903673i	0.997845	+	0.0656091i	$0.0208990\pi$
$242$	2.58410	+	0.839626i	0.166112	+	0.0539732i
$243$		−	15.8626i		−	1.01759i
$244$	1.26738	−	3.90061i	0.0811360	−	0.249711i
$245$	11.6677	+	9.83875i	0.745424	+	0.628575i
$246$	0.700662	+	2.15642i	0.0446726	+	0.137488i
$247$	−0.163775	+	0.0532136i	−0.0104207	+	0.00338590i
$248$	−29.4372	+	40.5168i	−1.86926	+	2.57282i
$249$	−12.5378			−0.794552
$250$	12.1534	+	27.8409i	0.768650	+	1.76081i
$251$	8.39999			0.530203			0.265101	−	0.964221i	$-0.414595\pi$
$251$	8.39999			0.530203			0.265101	+	0.964221i	$0.414595\pi$
$252$	−3.08937	+	4.25215i	−0.194612	+	0.267860i
$253$	−7.66759	+	2.49135i	−0.482057	+	0.156630i
$254$	−8.46799	−	26.0618i	−0.531329	−	1.63526i
$255$	9.51086	+	8.01998i	0.595593	+	0.502230i
$256$	10.1652	−	31.2854i	0.635328	−	1.95534i
$257$			2.92571i			0.182501i	0.995828	+	0.0912503i	$0.0290863\pi$
$257$			2.92571i			0.182501i	−0.995828	+	0.0912503i	$0.970914\pi$
$258$	2.63318	+	0.855571i	0.163935	+	0.0532656i
$259$	2.77173	−	2.01378i	0.172227	−	0.125130i
$260$	−33.8937	+	8.36333i	−2.10200	+	0.518671i
$261$	5.13956	+	3.73411i	0.318131	+	0.231136i
$262$	5.21340	+	7.17562i	0.322085	+	0.443312i
$263$	−15.9064	−	21.8933i	−0.980831	−	1.35000i	−0.936381	−	0.350986i	$-0.885846\pi$
$263$	−15.9064	−	21.8933i	−0.980831	−	1.35000i	−0.0444499	−	0.999012i	$-0.514154\pi$
$264$	−6.05171	−	4.39683i	−0.372457	−	0.270606i
$265$	6.92111	+	2.81587i	0.425160	+	0.172977i
$266$	0.0545156	−	0.0396079i	0.00334256	−	0.00242851i
$267$	3.38361	+	1.09940i	0.207074	+	0.0672823i
$268$			35.9804i			2.19785i
$269$	2.98880	−	9.19858i	0.182230	−	0.560847i	−0.817659	−	0.575702i	$-0.804729\pi$
$269$	2.98880	−	9.19858i	0.182230	−	0.560847i	0.999890	+	0.0148552i	$0.00472872\pi$
$270$	−9.94670	+	24.4479i	−0.605337	+	1.48785i
$271$	−1.12639	−	3.46667i	−0.0684233	−	0.210585i	0.910998	−	0.412410i	$-0.135313\pi$
$271$	−1.12639	−	3.46667i	−0.0684233	−	0.210585i	−0.979422	+	0.201825i	$0.935313\pi$
$272$	−92.3630	+	30.0106i	−5.60033	+	1.81966i
$273$	0.579655	−	0.797827i	0.0350823	−	0.0482867i
$274$	−23.6458			−1.42850
$275$	−2.21364	+	4.48328i	−0.133488	+	0.270352i
$276$	35.3194			2.12598
$277$	−5.56526	+	7.65993i	−0.334384	+	0.460241i	−0.942791	−	0.333385i	$-0.891809\pi$
$277$	−5.56526	+	7.65993i	−0.334384	+	0.460241i	0.608406	+	0.793626i	$0.291809\pi$
$278$	14.7216	−	4.78334i	0.882943	−	0.286886i
$279$	3.93618	+	12.1143i	0.235653	+	0.725264i
$280$	7.29138	−	4.53159i	0.435743	−	0.270814i
$281$	5.82286	−	17.9209i	0.347363	−	1.06907i	−0.612944	−	0.790127i	$-0.710015\pi$
$281$	5.82286	−	17.9209i	0.347363	−	1.06907i	0.960307	−	0.278946i	$-0.0899852\pi$
$282$		−	9.74043i		−	0.580034i
$283$	−29.3420	−	9.53378i	−1.74420	−	0.566725i	−0.748822	−	0.662771i	$-0.769380\pi$
$283$	−29.3420	−	9.53378i	−1.74420	−	0.566725i	−0.995377	+	0.0960465i	$0.969380\pi$
$284$	−56.5756	+	41.1046i	−3.35715	+	2.43911i
$285$	0.0696527	−	0.0826009i	0.00412587	−	0.00489286i
$286$	−6.37589	−	4.63236i	−0.377014	−	0.273917i
$287$	−0.251749	−	0.346503i	−0.0148603	−	0.0204534i
$288$	−27.7816	−	38.2381i	−1.63705	−	2.25320i
$289$	24.0517	+	17.4745i	1.41480	+	1.02791i
$290$	−8.71589	−	14.0240i	−0.511815	−	0.823515i
$291$	−12.4187	+	9.02272i	−0.727997	+	0.528921i
$292$	−29.6036	−	9.61879i	−1.73242	−	0.562897i
$293$		−	13.4568i		−	0.786156i	−0.919505	−	0.393078i	$-0.871410\pi$
$293$		−	13.4568i		−	0.786156i	0.919505	−	0.393078i	$-0.128590\pi$
$294$	4.66436	−	14.3554i	0.272031	−	0.837226i
$295$	−15.5144	−	1.12272i	−0.903282	−	0.0653671i
$296$	23.2930	+	71.6884i	1.35388	+	4.16680i
$297$	−4.13163	+	1.34245i	−0.239741	+	0.0778967i
$298$	6.60656	−	9.09315i	0.382708	−	0.526752i
$299$	23.3847			1.35237
$300$	15.2924	−	15.6826i	0.882905	−	0.905437i
$301$	−0.522995			−0.0301449
$302$	10.5479	−	14.5180i	0.606964	−	0.835415i
$303$	14.0013	−	4.54929i	0.804352	−	0.261350i
$304$	0.260639	+	0.802164i	0.0149487	+	0.0460073i
$305$	0.408176	+	1.65420i	0.0233721	+	0.0947192i
$306$	−13.4167	+	41.2923i	−0.766980	+	2.36052i
$307$		−	1.04303i		−	0.0595287i	−0.999557	−	0.0297644i	$-0.990524\pi$
$307$		−	1.04303i		−	0.0595287i	0.999557	−	0.0297644i	$-0.00947569\pi$
$308$	2.13842	+	0.694816i	0.121848	+	0.0395908i
$309$	−8.20167	+	5.95887i	−0.466577	+	0.338988i
$310$	2.38957	−	33.0204i	0.135718	−	1.87543i
$311$	12.0759	+	8.77366i	0.684762	+	0.497509i	0.874934	−	0.484242i	$-0.160905\pi$
$311$	12.0759	+	8.77366i	0.684762	+	0.497509i	−0.190172	+	0.981751i	$0.560905\pi$
$312$	12.7532	+	17.5533i	0.722008	+	0.993758i
$313$	2.08545	+	2.87038i	0.117877	+	0.162244i	0.863878	−	0.503701i	$-0.168029\pi$
$313$	2.08545	+	2.87038i	0.117877	+	0.162244i	−0.746001	+	0.665945i	$0.768029\pi$
$314$	9.87770	+	7.17657i	0.557431	+	0.404997i
$315$	0.157597	−	2.17778i	0.00887961	−	0.122704i
$316$	53.2964	−	38.7221i	2.99816	−	2.17829i
$317$	22.2928	+	7.24338i	1.25209	+	0.406829i	0.858669	−	0.512530i	$-0.171292\pi$
$317$	22.2928	+	7.24338i	1.25209	+	0.406829i	0.393420	+	0.919359i	$0.371292\pi$
$318$		−	7.38971i		−	0.414394i
$319$	0.839822	−	2.58471i	0.0470210	−	0.144716i
$320$	14.2091	+	57.5848i	0.794314	+	3.21909i
$321$	−1.25185	−	3.85278i	−0.0698712	−	0.215041i
$322$	−8.70284	+	2.82773i	−0.484991	+	0.157583i
$323$	0.238547	−	0.328332i	0.0132731	−	0.0182689i
$324$	−18.7146			−1.03970
$325$	10.1250	−	10.3834i	0.561632	−	0.575966i
$326$	−34.5812			−1.91528
$327$	−3.52920	+	4.85753i	−0.195165	+	0.268622i
$328$	8.96201	−	2.91193i	0.494844	−	0.160785i
$329$	0.568570	+	1.74988i	0.0313463	+	0.0964739i
$330$	4.93204	+	0.356913i	0.271500	+	0.0196474i
$331$	−4.00902	+	12.3385i	−0.220356	+	0.678185i	0.778374	+	0.627801i	$0.216045\pi$
$331$	−4.00902	+	12.3385i	−0.220356	+	0.678185i	−0.998730	+	0.0503844i	$0.983955\pi$
$332$			82.9161i			4.55061i
$333$	18.2332	+	5.92434i	0.999175	+	0.324652i
$334$	−0.310013	+	0.225237i	−0.0169631	+	0.0123244i
$335$	−7.89006	−	12.6952i	−0.431080	−	0.693613i
$336$	−3.90773	−	2.83913i	−0.213184	−	0.154888i
$337$	4.82646	+	6.64305i	0.262914	+	0.361870i	0.919982	−	0.391962i	$-0.128203\pi$
$337$	4.82646	+	6.64305i	0.262914	+	0.361870i	−0.657068	+	0.753832i	$0.728203\pi$
$338$	−7.32545	−	10.0826i	−0.398452	−	0.548422i
$339$	3.67205	+	2.66790i	0.199438	+	0.144901i
$340$	53.0383	−	62.8979i	2.87641	−	3.41112i
$341$	4.40845	−	3.20293i	0.238731	−	0.173448i
$342$	0.358619	+	0.116522i	0.0193919	+	0.00630082i
$343$			5.77537i			0.311841i
$344$	3.55573	−	10.9434i	0.191712	−	0.590030i
$345$	−12.4620	+	7.74511i	−0.670930	+	0.416983i
$346$	−14.6220	−	45.0018i	−0.786082	−	2.41931i
$347$	−21.8847	+	7.11078i	−1.17483	+	0.381727i	−0.830445	−	0.557101i	$-0.811914\pi$
$347$	−21.8847	+	7.11078i	−1.17483	+	0.381727i	−0.344389	+	0.938827i	$0.611914\pi$
$348$	−6.99817	+	9.63215i	−0.375141	+	0.516337i
$349$	29.3001			1.56840			0.784199	−	0.620509i	$-0.213074\pi$
$349$	29.3001			1.56840			0.784199	+	0.620509i	$0.213074\pi$
$350$	−2.51252	+	5.08860i	−0.134300	+	0.271997i
$351$	12.6007			0.672576
$352$	−11.8848	+	16.3581i	−0.633465	+	0.871889i
$353$	−2.84528	+	0.924488i	−0.151439	+	0.0492055i	−0.383756	−	0.923435i	$-0.625369\pi$
$353$	−2.84528	+	0.924488i	−0.151439	+	0.0492055i	0.232317	+	0.972640i	$0.425369\pi$
$354$	4.75381	+	14.6307i	0.252662	+	0.777613i
$355$	10.9482	−	26.9096i	0.581071	−	1.42821i
$356$	7.27065	−	22.3768i	0.385344	−	1.18597i
$357$			2.32416i			0.123008i
$358$	4.68192	+	1.52125i	0.247447	+	0.0804004i
$359$	22.4264	−	16.2937i	1.18362	−	0.859951i	0.191046	−	0.981581i	$-0.438812\pi$
$359$	22.4264	−	16.2937i	1.18362	−	0.859951i	0.992575	+	0.121630i	$0.0388122\pi$
$360$	44.4975	+	18.1039i	2.34522	+	0.954160i
$361$	15.3685	+	11.1658i	0.808867	+	0.587676i
$362$	9.31263	+	12.8177i	0.489461	+	0.673685i
$363$	0.478399	+	0.658460i	0.0251095	+	0.0345602i
$364$	−5.27625	−	3.83342i	−0.276551	−	0.200926i
$365$	12.5545	−	3.09785i	0.657133	−	0.162149i
$366$	1.36323	−	0.990447i	0.0712574	−	0.0517715i
$367$	−3.43511	−	1.11613i	−0.179311	−	0.0582617i	0.217985	−	0.975952i	$-0.430052\pi$
$367$	−3.43511	−	1.11613i	−0.179311	−	0.0582617i	−0.397296	+	0.917690i	$0.630052\pi$
$368$		−	114.538i		−	5.97070i
$369$	0.740622	−	2.27940i	0.0385552	−	0.118661i
$370$	−38.0934	−	32.1220i	−1.98038	−	1.66994i
$371$	0.431354	+	1.32757i	0.0223948	+	0.0689240i
$372$	−22.7036	+	7.37686i	−1.17713	+	0.382472i
$373$	12.9750	−	17.8586i	0.671821	−	0.924682i	−0.327979	−	0.944685i	$-0.606368\pi$
$373$	12.9750	−	17.8586i	0.671821	−	0.924682i	0.999800	+	0.0200028i	$0.00636751\pi$
$374$	18.5737			0.960424
$375$	−1.95669	+	8.88684i	−0.101043	+	0.458914i
$376$	−40.4810			−2.08765
$377$	−4.63344	+	6.37738i	−0.238634	+	0.328452i
$378$	−4.68947	+	1.52370i	−0.241200	+	0.0783707i
$379$	−2.64991	−	8.15559i	−0.136117	−	0.418924i	0.859645	−	0.510891i	$-0.170685\pi$
$379$	−2.64991	−	8.15559i	−0.136117	−	0.418924i	−0.995762	+	0.0919670i	$0.970685\pi$
$380$	−0.546263	−	0.460633i	−0.0280227	−	0.0236300i
$381$	2.53658	−	7.80680i	0.129953	−	0.399954i
$382$		−	21.9833i		−	1.12476i
$383$	−1.59112	−	0.516986i	−0.0813024	−	0.0264167i	0.268083	−	0.963396i	$-0.413610\pi$
$383$	−1.59112	−	0.516986i	−0.0813024	−	0.0264167i	−0.349386	+	0.936979i	$0.613610\pi$
$384$	20.8281	−	15.1325i	1.06288	−	0.772228i
$385$	−0.906879	+	0.223774i	−0.0462189	+	0.0114046i
$386$	58.5430	+	42.5340i	2.97976	+	2.16492i
$387$	−1.72021	−	2.36766i	−0.0874430	−	0.120355i
$388$	59.6697	+	82.1283i	3.02927	+	4.16943i
$389$	−13.4849	−	9.79734i	−0.683710	−	0.496745i	0.190876	−	0.981614i	$-0.438867\pi$
$389$	−13.4849	−	9.79734i	−0.683710	−	0.496745i	−0.874587	+	0.484869i	$0.838867\pi$
$390$	−13.2855	−	5.40525i	−0.672739	−	0.273705i
$391$	−44.5867	+	32.3942i	−2.25485	+	1.63824i
$392$	−59.6608	−	19.3850i	−3.01333	−	0.979089i
$393$			2.65687i			0.134021i
$394$	7.06949	−	21.7576i	0.356156	−	1.09613i
$395$	−10.3136	+	25.3499i	−0.518936	+	1.27549i
$396$	3.88807	+	11.9663i	0.195383	+	0.601327i
$397$	−14.2747	+	4.63813i	−0.716427	+	0.232781i	−0.644473	−	0.764627i	$-0.722923\pi$
$397$	−14.2747	+	4.63813i	−0.716427	+	0.232781i	−0.0719535	+	0.997408i	$0.522923\pi$
$398$	−21.8834	+	30.1199i	−1.09692	+	1.50978i
$399$	0.0201851			0.00101052
$400$	−50.8575	−	49.5918i	−2.54287	−	2.47959i
$401$	−5.08654			−0.254010			−0.127005	−	0.991902i	$-0.540536\pi$
$401$	−5.08654			−0.254010			−0.127005	+	0.991902i	$0.540536\pi$
$402$	−8.68903	+	11.9594i	−0.433369	+	0.596482i
$403$	−15.0319	+	4.88417i	−0.748794	+	0.243298i
$404$	−30.0857	−	92.5943i	−1.49682	−	4.60674i
$405$	6.60319	−	4.10388i	0.328115	−	0.203924i
$406$	0.953212	−	2.93369i	0.0473071	−	0.145596i
$407$		−	8.20151i		−	0.406534i
$408$	−48.6320	−	15.8015i	−2.40764	−	0.782291i
$409$	0.483104	−	0.350996i	0.0238880	−	0.0173556i	−0.575777	−	0.817607i	$-0.695300\pi$
$409$	0.483104	−	0.350996i	0.0238880	−	0.0173556i	0.599665	+	0.800251i	$0.295300\pi$
$410$	−4.01569	+	4.76219i	−0.198321	+	0.235188i
$411$	−5.73034	−	4.16334i	−0.282657	−	0.205362i
$412$	39.4076	+	54.2399i	1.94147	+	2.67221i
$413$	−1.70805	−	2.35093i	−0.0840478	−	0.115682i
$414$	−41.4264	−	30.0980i	−2.03600	−	1.47924i
$415$	−18.1825	−	29.2558i	−0.892543	−	1.43611i
$416$	47.4474	−	34.4726i	2.32630	−	1.69016i
$417$	4.40985	+	1.43285i	0.215951	+	0.0701668i
$418$		−	0.161311i		−	0.00788998i
$419$	7.70606	−	23.7168i	0.376466	−	1.15864i	−0.566019	−	0.824393i	$-0.691517\pi$
$419$	7.70606	−	23.7168i	0.376466	−	1.15864i	0.942484	−	0.334250i	$-0.108483\pi$
$420$	4.08141	+	0.295356i	0.199152	+	0.0144119i
$421$	−10.2330	−	31.4939i	−0.498726	−	1.53492i	−0.811069	−	0.584950i	$-0.801114\pi$
$421$	−10.2330	−	31.4939i	−0.498726	−	1.53492i	0.312343	−	0.949969i	$-0.398886\pi$
$422$	38.6794	−	12.5677i	1.88288	−	0.611786i
$423$	−6.05180	+	8.32959i	−0.294249	+	0.404999i
$424$	−30.7115			−1.49148
$425$	−4.92111	+	33.8234i	−0.238709	+	1.64067i
$426$	−28.7315			−1.39205
$427$	−0.187092	+	0.257510i	−0.00905401	+	0.0124618i
$428$	−25.4795	+	8.27880i	−1.23160	+	0.400171i
$429$	−0.729515	−	2.24522i	−0.0352213	−	0.108400i
$430$	1.82227	+	7.38503i	0.0878776	+	0.356138i
$431$	3.09201	−	9.51624i	0.148937	−	0.458381i	−0.848559	−	0.529100i	$-0.822529\pi$
$431$	3.09201	−	9.51624i	0.148937	−	0.458381i	0.997496	+	0.0707194i	$0.0225295\pi$
$432$		−	61.7179i		−	2.96941i
$433$	3.81442	+	1.23938i	0.183309	+	0.0595608i	0.399233	−	0.916849i	$-0.369276\pi$
$433$	3.81442	+	1.23938i	0.183309	+	0.0595608i	−0.215924	+	0.976410i	$0.569276\pi$
$434$	5.00367	−	3.63538i	0.240184	−	0.174504i
$435$	0.356996	−	4.93319i	0.0171167	−	0.236528i
$436$	32.1242	+	23.3396i	1.53847	+	1.11776i
$437$	0.281340	+	0.387232i	0.0134583	+	0.0185238i
$438$	−7.51698	−	10.3462i	−0.359175	−	0.494362i
$439$	−21.6952	−	15.7625i	−1.03545	−	0.752301i	−0.0660604	−	0.997816i	$-0.521043\pi$
$439$	−21.6952	−	15.7625i	−1.03545	−	0.752301i	−0.969393	+	0.245515i	$0.921043\pi$
$440$	1.48332	−	20.4974i	0.0707146	−	0.977176i
$441$	−12.9079	+	9.37814i	−0.614662	+	0.446578i
$442$	−51.2372	−	16.6480i	−2.43710	−	0.791863i
$443$			28.8211i			1.36933i	0.728857	+	0.684666i	$0.240052\pi$
$443$			28.8211i			1.36933i	−0.728857	+	0.684666i	$0.759948\pi$
$444$	−11.1029	+	34.1712i	−0.526921	+	1.62170i
$445$	2.34160	+	9.48971i	0.111002	+	0.449855i
$446$	−10.5110	−	32.3497i	−0.497713	−	1.53180i
$447$	3.20208	−	1.04042i	0.151453	−	0.0492101i
$448$	−6.51290	+	8.96424i	−0.307706	+	0.423521i
$449$	−16.8676			−0.796031			−0.398015	−	0.917379i	$-0.630301\pi$
$449$	−16.8676			−0.796031			−0.398015	+	0.917379i	$0.630301\pi$
$450$	−31.3008	+	5.36263i	−1.47553	+	0.252797i
$451$	−1.02530			−0.0482795
$452$	17.6436	−	24.2843i	0.829884	−	1.14224i
$453$	5.11238	−	1.66111i	0.240200	−	0.0780459i
$454$	5.18972	+	15.9723i	0.243565	+	0.749617i
$455$	2.70228	+	0.195554i	0.126685	+	0.00916769i
$456$	−0.137235	+	0.422364i	−0.00642660	+	0.0197790i
$457$			22.1146i			1.03448i	0.855841	+	0.517240i	$0.173040\pi$
$457$			22.1146i			1.03448i	−0.855841	+	0.517240i	$0.826960\pi$
$458$	30.3746	+	9.86929i	1.41931	+	0.461162i
$459$	−24.0253	+	17.4554i	−1.12140	+	0.814747i
$460$	51.2206	+	82.4145i	2.38817	+	3.84260i
$461$	−17.4171	−	12.6543i	−0.811196	−	0.589368i	0.102981	−	0.994683i	$-0.467162\pi$
$461$	−17.4171	−	12.6543i	−0.811196	−	0.589368i	−0.914177	+	0.405315i	$0.867162\pi$
$462$	0.542992	+	0.747364i	0.0252623	+	0.0347705i
$463$	7.60350	+	10.4653i	0.353364	+	0.486364i	0.948285	−	0.317420i	$-0.102817\pi$
$463$	7.60350	+	10.4653i	0.353364	+	0.486364i	−0.594921	+	0.803784i	$0.702817\pi$
$464$	31.2363	+	22.6945i	1.45011	+	1.05356i
$465$	6.39302	−	7.58146i	0.296469	−	0.351582i
$466$	52.8172	−	38.3739i	2.44671	−	1.77764i
$467$	15.1652	+	4.92746i	0.701760	+	0.228016i	0.638097	−	0.769956i	$-0.279722\pi$
$467$	15.1652	+	4.92746i	0.701760	+	0.228016i	0.0636627	+	0.997971i	$0.479722\pi$
$468$		−	36.4949i		−	1.68698i
$469$	0.862896	−	2.65572i	0.0398448	−	0.122630i
$470$	22.7284	−	14.1257i	1.04838	−	0.651569i
$471$	1.13018	+	3.47835i	0.0520761	+	0.160274i
$472$	60.8049	−	19.7567i	2.79877	−	0.909376i
$473$	−0.735897	+	1.01288i	−0.0338366	+	0.0465721i
$474$	27.0662			1.24319
$475$	0.293753	+	0.0427394i	0.0134783	+	0.00196102i
$476$	15.3703			0.704498
$477$	−4.59129	+	6.31936i	−0.210221	+	0.289344i
$478$	19.3812	−	6.29734i	0.886477	−	0.288034i
$479$	5.87995	+	18.0966i	0.268662	+	0.826855i	0.990827	+	0.135135i	$0.0431468\pi$
$479$	5.87995	+	18.0966i	0.268662	+	0.826855i	−0.722166	+	0.691720i	$0.756853\pi$
$480$	−13.8678	+	34.0856i	−0.632975	+	1.55579i
$481$	−7.35116	+	22.6246i	−0.335184	+	1.03159i
$482$		−	64.8492i		−	2.95380i
$483$	−2.60693	−	0.847044i	−0.118620	−	0.0385418i
$484$	4.35458	−	3.16379i	0.197935	−	0.143809i
$485$	−39.0634	−	15.8930i	−1.77378	−	0.721666i
$486$	−34.8687	−	25.3336i	−1.58168	−	1.14916i
$487$	24.2576	+	33.3877i	1.09922	+	1.51294i	0.836418	+	0.548092i	$0.184646\pi$
$487$	24.2576	+	33.3877i	1.09922	+	1.51294i	0.262799	+	0.964851i	$0.415354\pi$
$488$	−4.11628	−	5.66557i	−0.186335	−	0.256468i
$489$	−8.38043	−	6.08874i	−0.378976	−	0.275342i
$490$	40.2614	−	9.93455i	1.81882	−	0.448797i
$491$	−11.6719	+	8.48014i	−0.526746	+	0.382703i	−0.819139	−	0.573595i	$-0.805548\pi$
$491$	−11.6719	+	8.48014i	−0.526746	+	0.382703i	0.292393	+	0.956298i	$0.405548\pi$
$492$	4.27187	+	1.38801i	0.192591	+	0.0625765i
$493$		−	18.5781i		−	0.836714i
$494$	−0.144586	+	0.444990i	−0.00650523	+	0.0200210i
$495$	−3.99591	−	3.36953i	−0.179603	−	0.151449i
$496$	23.9225	+	73.6260i	1.07415	+	3.30591i
$497$	5.16165	−	1.67712i	0.231532	−	0.0752292i
$498$	−20.0237	+	27.5603i	−0.897283	+	1.23500i
$499$	−25.5843			−1.14531			−0.572655	−	0.819796i	$-0.694087\pi$
$499$	−25.5843			−1.14531			−0.572655	+	0.819796i	$0.694087\pi$
$500$	58.7711	+	12.9402i	2.62832	+	0.578701i
$501$	−0.114786			−0.00512828
$502$	13.4153	−	18.4646i	0.598755	−	0.824115i
$503$	−11.9389	+	3.87918i	−0.532328	+	0.172964i	−0.562833	−	0.826571i	$-0.690289\pi$
$503$	−11.9389	+	3.87918i	−0.532328	+	0.172964i	0.0305048	+	0.999535i	$0.490289\pi$
$504$	2.77328	+	8.53527i	0.123532	+	0.380191i
$505$	30.9201	+	26.0732i	1.37593	+	1.16024i
$506$	−6.76921	+	20.8335i	−0.300928	+	0.926162i
$507$		−	3.73323i		−	0.165798i
$508$	−51.6285	−	16.7751i	−2.29064	−	0.744275i
$509$	14.3664	−	10.4378i	0.636780	−	0.462647i	−0.221963	−	0.975055i	$-0.571246\pi$
$509$	14.3664	−	10.4378i	0.636780	−	0.462647i	0.858742	+	0.512408i	$0.171246\pi$
$510$	32.8187	−	8.09807i	1.45324	−	0.358588i
$511$	1.95437	+	1.41993i	0.0864561	+	0.0628140i
$512$	−15.3510	−	21.1288i	−0.678423	−	0.933769i
$513$	0.151598	+	0.208657i	0.00669323	+	0.00921244i
$514$	6.43120	+	4.67254i	0.283668	+	0.206097i
$515$	−25.7986	−	10.4962i	−1.13682	−	0.462519i
$516$	4.43728	−	3.22387i	0.195340	−	0.141923i
$517$	4.18899	+	1.36108i	0.184231	+	0.0598604i
$518$		−	9.30885i		−	0.409007i
$519$	4.38001	−	13.4803i	0.192261	−	0.591718i
$520$	−22.4641	+	55.2143i	−0.985115	+	2.42131i
$521$	4.71524	+	14.5120i	0.206578	+	0.635783i	0.999645	+	0.0266479i	$0.00848330\pi$
$521$	4.71524	+	14.5120i	0.206578	+	0.635783i	−0.793066	+	0.609135i	$0.791517\pi$
$522$	16.4164	−	5.33401i	0.718527	−	0.233463i
$523$	4.15279	−	5.71582i	0.181589	−	0.249936i	−0.708513	−	0.705698i	$-0.750633\pi$
$523$	4.15279	−	5.71582i	0.181589	−	0.249936i	0.890101	+	0.455763i	$0.150633\pi$
$524$	17.5706			0.767576
$525$	−1.50484	+	0.790791i	−0.0656766	+	0.0345130i
$526$	−73.5287			−3.20600
$527$	21.8949	−	30.1357i	0.953756	−	1.31273i
$528$	−10.9970	+	3.57315i	−0.478584	+	0.155501i
$529$	−12.9783	−	39.9432i	−0.564275	−	1.73666i
$530$	17.2432	−	10.7166i	0.748997	−	0.465501i
$531$	5.02492	−	15.4651i	0.218063	−	0.671129i
$532$		−	0.133490i		−	0.00578752i
$533$	2.82837	+	0.918995i	0.122511	+	0.0398061i
$534$	7.82052	−	5.68194i	0.338427	−	0.245881i
$535$	7.17467	−	8.50842i	0.310188	−	0.367851i
$536$	49.7031	+	36.1114i	2.14685	+	1.55978i
$537$	0.866772	+	1.19301i	0.0374040	+	0.0514821i
$538$	−15.4467	−	21.2606i	−0.665956	−	0.916609i
$539$	5.52194	+	4.01193i	0.237847	+	0.172806i
$540$	27.5999	+	44.4085i	1.18771	+	1.91104i
$541$	−34.1877	+	24.8388i	−1.46984	+	1.06790i	−0.489184	+	0.872181i	$0.662705\pi$
$541$	−34.1877	+	24.8388i	−1.46984	+	1.06790i	−0.980659	+	0.195723i	$0.937295\pi$
$542$	−9.41924	−	3.06050i	−0.404591	−	0.131460i
$543$			4.74594i			0.203668i
$544$	−42.7123	+	131.455i	−1.83127	+	5.63608i
$545$	−16.4527	−	1.19062i	−0.704756	−	0.0510005i
$546$	−0.828012	−	2.54836i	−0.0354356	−	0.109060i
$547$	−6.86653	+	2.23107i	−0.293592	+	0.0953937i	−0.452110	−	0.891962i	$-0.649328\pi$
$547$	−6.86653	+	2.23107i	−0.293592	+	0.0953937i	0.158518	+	0.987356i	$0.449328\pi$
$548$	−27.5333	+	37.8963i	−1.17616	+	1.61885i
$549$	−1.78115			−0.0760177
$550$	6.31967	+	12.0260i	0.269472	+	0.512792i
$551$	−0.161349			−0.00687369
$552$	35.4480	−	48.7900i	1.50877	−	2.07664i
$553$	−4.86247	+	1.57991i	−0.206773	+	0.0671848i
$554$	7.94974	+	24.4668i	0.337752	+	1.03949i
$555$	−3.57582	−	14.4916i	−0.151785	−	0.615134i
$556$	9.47581	−	29.1636i	0.401864	−	1.23681i
$557$		−	9.60346i		−	0.406912i	−0.979084	−	0.203456i	$-0.934783\pi$
$557$		−	9.60346i		−	0.406912i	0.979084	−	0.203456i	$-0.0652173\pi$
$558$	32.9156	+	10.6949i	1.39343	+	0.452752i
$559$	2.93789	−	2.13450i	0.124260	−	0.0902799i
$560$	0.957816	−	13.2357i	0.0404751	−	0.559309i
$561$	4.50117	+	3.27029i	0.190039	+	0.138072i
$562$	−30.0937	−	41.4205i	−1.26943	−	1.74722i
$563$	10.8398	+	14.9197i	0.456844	+	0.628792i	0.973851	−	0.227189i	$-0.0729536\pi$
$563$	10.8398	+	14.9197i	0.456844	+	0.628792i	−0.517006	+	0.855982i	$0.672954\pi$
$564$	−15.6106	−	11.3418i	−0.657327	−	0.477576i
$565$	−0.900049	+	12.4374i	−0.0378653	+	0.523246i
$566$	−67.8178	+	49.2725i	−2.85060	+	2.07108i
$567$	1.38133	+	0.448821i	0.0580103	+	0.0188487i
$568$			119.408i			5.01023i
$569$	−5.72554	+	17.6214i	−0.240027	+	0.738728i	0.756387	+	0.654124i	$0.226963\pi$
$569$	−5.72554	+	17.6214i	−0.240027	+	0.738728i	−0.996415	+	0.0846041i	$0.973037\pi$
$570$	−0.0703309	−	0.285027i	−0.00294584	−	0.0119385i
$571$	7.11975	+	21.9123i	0.297952	+	0.917003i	0.982214	+	0.187766i	$0.0601247\pi$
$571$	7.11975	+	21.9123i	0.297952	+	0.917003i	−0.684262	+	0.729237i	$0.739875\pi$
$572$	−14.8482	+	4.82448i	−0.620836	+	0.201722i
$573$	3.87062	−	5.32745i	0.161697	−	0.222557i
$574$	−1.16373			−0.0485732
$575$	−36.1450	−	17.8468i	−1.50735	−	0.744263i
$576$	−62.0041			−2.58350
$577$	−25.0159	+	34.4315i	−1.04143	+	1.43340i	−0.145416	+	0.989371i	$0.546452\pi$
$577$	−25.0159	+	34.4315i	−1.04143	+	1.43340i	−0.896012	+	0.444031i	$0.853548\pi$
$578$	76.8240	−	24.9616i	3.19546	−	1.03827i
$579$	6.69836	+	20.6154i	0.278374	+	0.856748i
$580$	−32.6245	−	2.36092i	−1.35466	−	0.0980317i
$581$	1.98853	−	6.12006i	0.0824980	−	0.253903i
$582$			41.7083i			1.72886i
$583$	3.17803	+	1.03261i	0.131621	+	0.0427662i
$584$	−42.9987	+	31.2404i	−1.77930	+	1.29274i
$585$	8.00289	+	12.8767i	0.330879	+	0.532388i
$586$	−29.5804	−	21.4914i	−1.22195	−	0.887802i
$587$	−16.9334	−	23.3068i	−0.698916	−	0.961976i	−0.999965	−	0.00836712i	$-0.997337\pi$
$587$	−16.9334	−	23.3068i	−0.698916	−	0.961976i	0.301049	−	0.953609i	$-0.402663\pi$
$588$	−17.5757	−	24.1909i	−0.724811	−	0.997617i
$589$	−0.261726	−	0.190155i	−0.0107842	−	0.00783520i
$590$	−27.2454	+	32.3102i	−1.12167	+	1.33019i
$591$	5.54411	−	4.02803i	0.228054	−	0.165691i
$592$	110.814	+	36.0058i	4.55445	+	1.47983i
$593$			24.8764i			1.02155i	0.859714	+	0.510776i	$0.170642\pi$
$593$			24.8764i			1.02155i	−0.859714	+	0.510776i	$0.829358\pi$
$594$	−3.64755	+	11.2260i	−0.149661	+	0.460608i
$595$	−5.42321	+	3.37053i	−0.222330	+	0.138178i
$596$	−6.88057	−	21.1762i	−0.281839	−	0.867412i
$597$	−10.6065	+	3.44625i	−0.434094	+	0.141046i
$598$	37.3469	−	51.4036i	1.52723	−	2.10205i
$599$	28.7886			1.17627			0.588136	−	0.808762i	$-0.299862\pi$
$599$	28.7886			1.17627			0.588136	+	0.808762i	$0.299862\pi$
$600$	−6.31585	−	36.8645i	−0.257843	−	1.50499i
$601$	31.1241			1.26958			0.634790	−	0.772685i	$-0.281087\pi$
$601$	31.1241			1.26958			0.634790	+	0.772685i	$0.281087\pi$
$602$	−0.835256	+	1.14963i	−0.0340425	+	0.0468555i
$603$	14.8610	−	4.82862i	0.605185	−	0.196637i
$604$	−10.9854	−	33.8096i	−0.446989	−	1.37569i
$605$	−0.842675	+	2.07121i	−0.0342596	+	0.0842065i
$606$	12.3608	−	38.0427i	0.502124	−	1.54538i
$607$			8.86129i			0.359669i	0.983697	+	0.179834i	$0.0575562\pi$
$607$			8.86129i			0.359669i	−0.983697	+	0.179834i	$0.942444\pi$
$608$	1.14167	+	0.370952i	0.0463010	+	0.0150441i
$609$	0.747539	−	0.543119i	0.0302918	−	0.0220083i
$610$	4.28809	+	1.74462i	0.173620	+	0.0706376i
$611$	−10.3357	−	7.50933i	−0.418138	−	0.303795i
$612$	50.5552	+	69.5833i	2.04357	+	2.81274i
$613$	−16.0512	−	22.0925i	−0.648301	−	0.892310i	0.350723	−	0.936479i	$-0.385936\pi$
$613$	−16.0512	−	22.0925i	−0.648301	−	0.892310i	−0.999024	+	0.0441696i	$0.985936\pi$
$614$	−2.29275	−	1.66578i	−0.0925279	−	0.0672255i
$615$	−1.81165	+	0.447026i	−0.0730526	+	0.0180258i
$616$	3.10603	−	2.25666i	0.125145	−	0.0909234i
$617$	−11.8828	−	3.86096i	−0.478384	−	0.155436i	0.0598921	−	0.998205i	$-0.480924\pi$
$617$	−11.8828	−	3.86096i	−0.478384	−	0.155436i	−0.538276	+	0.842768i	$0.680924\pi$
$618$			27.5453i			1.10804i
$619$	1.42397	−	4.38254i	0.0572343	−	0.176149i	−0.918352	−	0.395764i	$-0.870480\pi$
$619$	1.42397	−	4.38254i	0.0572343	−	0.176149i	0.975587	+	0.219615i	$0.0704800\pi$
$620$	−50.1383	−	42.2788i	−2.01360	−	1.69796i
$621$	−10.8231	−	33.3099i	−0.434314	−	1.33668i
$622$	38.5720	−	12.5328i	1.54660	−	0.502519i
$623$	−1.07330	+	1.47727i	−0.0430007	+	0.0591854i
$624$	33.5389			1.34263
$625$	−23.5742	+	8.32203i	−0.942969	+	0.332881i
$626$	9.64019			0.385299
$627$	0.0284022	−	0.0390922i	0.00113427	−	0.00156119i
$628$	23.0033	−	7.47422i	0.917930	−	0.298254i
$629$	−17.3249	−	53.3207i	−0.690790	−	2.12603i
$630$	−4.53543	−	3.82447i	−0.180696	−	0.152371i
$631$	−14.0716	+	43.3080i	−0.560183	+	1.72407i	0.121664	+	0.992571i	$0.461177\pi$
$631$	−14.0716	+	43.3080i	−0.560183	+	1.72407i	−0.681847	+	0.731494i	$0.738823\pi$
$632$		−	112.487i		−	4.47447i
$633$	11.5864	+	3.76465i	0.460518	+	0.149631i
$634$	51.5252	−	37.4353i	2.04633	−	1.48674i
$635$	21.8950	−	5.40263i	0.868877	−	0.214397i
$636$	−11.8432	−	8.60461i	−0.469615	−	0.341195i
$637$	−11.6368	−	16.0167i	−0.461066	−	0.634603i
$638$	−4.34037	−	5.97401i	−0.171837	−	0.236513i
$639$	24.5699	+	17.8511i	0.971972	+	0.706179i
$640$	65.5155	+	26.6551i	2.58973	+	1.05364i
$641$	−30.1249	+	21.8870i	−1.18986	+	0.864486i	−0.993250	−	0.115995i	$-0.962994\pi$
$641$	−30.1249	+	21.8870i	−1.18986	+	0.864486i	−0.196613	+	0.980481i	$0.562994\pi$
$642$	−10.4683	−	3.40137i	−0.413153	−	0.134241i
$643$			29.7652i			1.17382i	0.809651	+	0.586912i	$0.199657\pi$
$643$			29.7652i			1.17382i	−0.809651	+	0.586912i	$0.800343\pi$
$644$	−5.60173	+	17.2404i	−0.220739	+	0.679366i
$645$	−0.858679	+	2.11054i	−0.0338105	+	0.0831025i
$646$	−0.340755	−	1.04873i	−0.0134068	−	0.0412619i
$647$	−10.8973	+	3.54074i	−0.428416	+	0.139201i	−0.515285	−	0.857019i	$-0.672314\pi$
$647$	−10.8973	+	3.54074i	−0.428416	+	0.139201i	0.0868689	+	0.996220i	$0.472314\pi$
$648$	−18.7827	+	25.8522i	−0.737856	+	1.01557i
$649$	−6.95639			−0.273062
$650$	−6.65418	−	38.8393i	−0.260998	−	1.52340i
$651$	1.85268			0.0726121
$652$	−40.2665	+	55.4221i	−1.57696	+	2.17050i
$653$	−14.5139	+	4.71587i	−0.567974	+	0.184546i	−0.578906	−	0.815394i	$-0.696520\pi$
$653$	−14.5139	+	4.71587i	−0.567974	+	0.184546i	0.0109317	+	0.999940i	$0.496520\pi$
$654$	5.04131	+	15.5156i	0.197131	+	0.606707i
$655$	−6.19956	+	3.85303i	−0.242237	+	0.150550i
$656$	4.50121	−	13.8533i	0.175743	−	0.540881i
$657$			13.5180i			0.527388i
$658$	4.75457	+	1.54485i	0.185352	+	0.0602247i
$659$	−7.91965	+	5.75396i	−0.308506	+	0.224142i	−0.731255	−	0.682104i	$-0.761065\pi$
$659$	−7.91965	+	5.75396i	−0.308506	+	0.224142i	0.422749	+	0.906247i	$0.361065\pi$
$660$	6.31490	−	7.48881i	0.245807	−	0.291502i
$661$	−23.3076	−	16.9340i	−0.906562	−	0.658656i	0.0335812	−	0.999436i	$-0.489309\pi$
$661$	−23.3076	−	16.9340i	−0.906562	−	0.658656i	−0.940143	+	0.340780i	$0.889309\pi$
$662$	20.7194	+	28.5179i	0.805284	+	1.10838i
$663$	−9.48563	−	13.0558i	−0.368391	−	0.507047i
$664$	114.540	+	83.2180i	4.44501	+	3.22949i
$665$	0.0292727	+	0.0471001i	0.00113515	+	0.00182646i
$666$	42.1423	−	30.6182i	1.63298	−	1.18643i
$667$	20.8384	+	6.77080i	0.806865	+	0.262166i
$668$			0.759114i			0.0293710i
$669$	3.14858	−	9.69033i	0.121731	−	0.374650i
$670$	−40.5071	−	2.93135i	−1.56493	−	0.113248i
$671$	0.235461	+	0.724676i	0.00908989	+	0.0279758i
$672$	−6.53811	+	2.12436i	−0.252213	+	0.0819490i
$673$	9.02295	−	12.4190i	0.347809	−	0.478718i	−0.598893	−	0.800829i	$-0.704392\pi$
$673$	9.02295	−	12.4190i	0.347809	−	0.478718i	0.946702	+	0.322111i	$0.104392\pi$
$674$	22.3107			0.859376
$675$	−19.4765	−	9.61663i	−0.749650	−	0.370144i
$676$	−24.6888			−0.949571
$677$	−8.43583	+	11.6109i	−0.324215	+	0.446244i	−0.939748	−	0.341867i	$-0.888941\pi$
$677$	−8.43583	+	11.6109i	−0.324215	+	0.446244i	0.615533	+	0.788111i	$0.288941\pi$
$678$	11.7290	−	3.81098i	0.450449	−	0.146360i
$679$	−2.43460	−	7.49293i	−0.0934314	−	0.287552i
$680$	−33.6554	−	136.394i	−1.29062	−	5.23046i
$681$	−1.55458	+	4.78450i	−0.0595715	+	0.183342i
$682$		−	14.8058i		−	0.566944i
$683$	20.0492	+	6.51438i	0.767161	+	0.249266i	0.666349	−	0.745640i	$-0.267856\pi$
$683$	20.0492	+	6.51438i	0.767161	+	0.249266i	0.100812	+	0.994906i	$0.467856\pi$
$684$	0.604325	−	0.439068i	0.0231069	−	0.0167882i
$685$	1.40455	−	19.4089i	0.0536651	−	0.741577i
$686$	12.6952	+	9.22363i	0.484706	+	0.352160i
$687$	5.62330	+	7.73980i	0.214542	+	0.295292i
$688$	−10.4547	−	14.3897i	−0.398584	−	0.548603i
$689$	−7.84133	−	5.69706i	−0.298731	−	0.217041i
$690$	−2.87750	+	39.7630i	−0.109544	+	1.51375i
$691$	4.16921	−	3.02911i	0.158604	−	0.115233i	−0.505652	−	0.862737i	$-0.668748\pi$
$691$	4.16921	−	3.02911i	0.158604	−	0.115233i	0.664257	+	0.747504i	$0.268748\pi$
$692$	−89.1488	−	28.9662i	−3.38893	−	1.10113i
$693$		−	0.976478i		−	0.0370933i
$694$	−19.3206	+	59.4627i	−0.733400	+	2.25717i
$695$	3.05180	+	12.3679i	0.115761	+	0.469141i
$696$	6.28214	+	19.3344i	0.238124	+	0.732870i
$697$	−6.66580	+	2.16585i	−0.252485	+	0.0820374i
$698$	46.7941	−	64.4066i	1.77118	−	2.43782i
$699$	19.5563			0.739686
$700$	5.22972	+	9.95192i	0.197665	+	0.376147i
$701$	24.4958			0.925195			0.462597	−	0.886568i	$-0.346918\pi$
$701$	24.4958			0.925195			0.462597	+	0.886568i	$0.346918\pi$
$702$	20.1241	−	27.6985i	0.759536	−	1.04541i
$703$	−0.463085	+	0.150465i	−0.0174656	+	0.00567491i
$704$	8.19670	+	25.2269i	0.308925	+	0.950773i
$705$	7.99513	+	0.578577i	0.301114	+	0.0217905i
$706$	−2.51191	+	7.73087i	−0.0945371	+	0.290955i
$707$			7.55593i			0.284170i
$708$	28.9835	+	9.41730i	1.08927	+	0.353924i
$709$	36.9518	−	26.8470i	1.38775	−	1.00826i	0.391645	−	0.920116i	$-0.371906\pi$
$709$	36.9518	−	26.8470i	1.38775	−	1.00826i	0.996108	−	0.0881450i	$-0.0280939\pi$
$710$	−41.6668	−	67.0423i	−1.56373	−	2.51605i
$711$	−23.1459	−	16.8164i	−0.868037	−	0.630666i
$712$	−23.6140	−	32.5019i	−0.884972	−	1.21806i
$713$	25.8226	+	35.5418i	0.967064	+	1.33105i
$714$	5.10890	+	3.71183i	0.191196	+	0.138912i
$715$	4.18105	−	4.95829i	0.156362	−	0.185430i
$716$	7.88970	−	5.73220i	0.294852	−	0.214222i
$717$	5.80564	+	1.88637i	0.216815	+	0.0704476i
$718$		−	75.3192i		−	2.81089i
$719$	−13.2018	+	40.6309i	−0.492343	+	1.51528i	0.328715	+	0.944429i	$0.393385\pi$
$719$	−13.2018	+	40.6309i	−0.492343	+	1.51528i	−0.821057	+	0.570846i	$0.806615\pi$
$720$	63.0699	−	39.1979i	2.35048	−	1.46082i
$721$	−1.60788	−	4.94855i	−0.0598807	−	0.184294i
$722$	49.0888	−	15.9499i	1.82690	−	0.593595i
$723$	11.4180	−	15.7156i	0.424642	−	0.584469i
$724$	31.3862			1.16646
$725$	12.0289	−	6.32115i	0.446740	−	0.234762i
$726$	2.21144			0.0820743
$727$	−23.8110	+	32.7730i	−0.883100	+	1.21548i	0.0924530	+	0.995717i	$0.470529\pi$
$727$	−23.8110	+	32.7730i	−0.883100	+	1.21548i	−0.975553	+	0.219765i	$0.929471\pi$
$728$	−10.5909	+	3.44120i	−0.392526	+	0.127539i
$729$	−0.766337	−	2.35854i	−0.0283829	−	0.0873534i
$730$	13.2408	−	32.5444i	0.490063	−	1.20452i
$731$	−2.64470	+	8.13955i	−0.0978177	+	0.301052i
$732$		−	3.33809i		−	0.123379i
$733$	3.67114	+	1.19283i	0.135597	+	0.0440581i	0.376029	−	0.926608i	$-0.377289\pi$
$733$	3.67114	+	1.19283i	0.135597	+	0.0440581i	−0.240432	+	0.970666i	$0.577289\pi$
$734$	−7.93953	+	5.76841i	−0.293053	+	0.212916i
$735$	11.5061	+	4.68130i	0.424411	+	0.172672i
$736$	−131.882	−	95.8178i	−4.86123	−	3.53189i
$737$	−3.92913	−	5.40798i	−0.144731	−	0.199205i
$738$	−3.82769	−	5.26836i	−0.140899	−	0.193931i
$739$	31.4015	+	22.8146i	1.15512	+	0.839247i	0.989154	−	0.146884i	$-0.0469243\pi$
$739$	31.4015	+	22.8146i	1.15512	+	0.839247i	0.165971	+	0.986131i	$0.446924\pi$
$740$	−95.8370	+	23.6479i	−3.52304	+	0.869315i
$741$	−0.113389	+	0.0823818i	−0.00416544	+	0.00302637i
$742$	3.60712	+	1.17202i	0.132422	+	0.0430264i
$743$		−	1.38009i		−	0.0506305i	−0.999680	−	0.0253152i	$-0.991941\pi$
$743$		−	1.38009i		−	0.0506305i	0.999680	−	0.0253152i	$-0.00805895\pi$
$744$	−12.5960	+	38.7664i	−0.461791	+	1.42125i
$745$	7.07141	+	5.96292i	0.259076	+	0.218465i
$746$	−18.5343	−	57.0426i	−0.678587	−	2.08848i
$747$	34.2468	−	11.1275i	1.25302	−	0.407132i
$748$	21.6273	−	29.7675i	0.790773	−	1.08841i
$749$	2.07920			0.0759722
$750$	16.4098	+	18.4940i	0.599201	+	0.675305i
$751$	14.8303			0.541165			0.270583	−	0.962697i	$-0.412784\pi$
$751$	14.8303			0.541165			0.270583	+	0.962697i	$0.412784\pi$
$752$	−36.7805	+	50.6240i	−1.34125	+	1.84607i
$753$	6.50215	−	2.11268i	0.236952	−	0.0769902i
$754$	6.61867	+	20.3702i	0.241038	+	0.741838i
$755$	11.2901	+	9.52029i	0.410888	+	0.346479i
$756$	−3.01846	+	9.28986i	−0.109780	+	0.337869i
$757$			8.33117i			0.302802i	0.988472	+	0.151401i	$0.0483784\pi$
$757$			8.33117i			0.302802i	−0.988472	+	0.151401i	$0.951622\pi$
$758$	−22.1594	−	7.20004i	−0.804867	−	0.261517i
$759$	−5.30863	+	3.85694i	−0.192691	+	0.139998i
$760$	−1.18457	+	0.292294i	−0.0429688	+	0.0106026i
$761$	−12.6014	−	9.15545i	−0.456800	−	0.331885i	0.335474	−	0.942049i	$-0.391103\pi$
$761$	−12.6014	−	9.15545i	−0.456800	−	0.331885i	−0.792275	+	0.610164i	$0.791103\pi$
$762$	−13.1096	−	18.0438i	−0.474910	−	0.653657i
$763$	−1.81135	−	2.49312i	−0.0655755	−	0.0902569i
$764$	−35.2319	−	25.5975i	−1.27464	−	0.926084i
$765$	−33.0965	−	13.4654i	−1.19661	−	0.486843i
$766$	−3.67754	+	2.67189i	−0.132875	+	0.0965392i
$767$	19.1898	+	6.23514i	0.692903	+	0.225138i
$768$		−	26.7736i		−	0.966111i
$769$	−7.90130	+	24.3177i	−0.284928	+	0.876919i	0.701492	+	0.712677i	$0.252518\pi$
$769$	−7.90130	+	24.3177i	−0.284928	+	0.876919i	−0.986420	+	0.164241i	$0.947482\pi$
$770$	−0.956451	+	2.35085i	−0.0344681	+	0.0847189i
$771$	0.735843	+	2.26469i	0.0265007	+	0.0815609i
$772$	136.335	−	44.2981i	4.90682	−	1.59432i
$773$	2.40887	−	3.31552i	0.0866410	−	0.119251i	−0.763496	−	0.645812i	$-0.776519\pi$
$773$	2.40887	−	3.31552i	0.0866410	−	0.119251i	0.850137	+	0.526561i	$0.176519\pi$
$774$	−7.95180			−0.285822
$775$	26.9619	+	3.92280i	0.968499	+	0.140911i
$776$	173.339			6.22249
$777$	1.63902	−	2.25591i	0.0587994	−	0.0809304i
$778$	−43.0724	+	13.9951i	−1.54422	+	0.501748i
$779$	0.0188102	+	0.0578919i	0.000673946	+	0.00207419i
$780$	−24.1325	+	14.9984i	−0.864083	+	0.537028i
$781$	4.01481	−	12.3563i	0.143661	−	0.442144i
$782$			149.745i			5.35486i
$783$	11.2286	+	3.64840i	0.401278	+	0.130383i
$784$	−78.4492	+	56.9967i	−2.80176	+	2.03560i
$785$	−6.47739	+	7.68152i	−0.231188	+	0.274165i
$786$	5.84025	+	4.24319i	0.208315	+	0.151350i
$787$	−15.0722	−	20.7451i	−0.537266	−	0.739483i	0.450950	−	0.892549i	$-0.351085\pi$
$787$	−15.0722	−	20.7451i	−0.537266	−	0.739483i	−0.988216	+	0.153066i	$0.951085\pi$
$788$	−26.6385	−	36.6647i	−0.948957	−	1.30613i
$789$	−17.8190	−	12.9462i	−0.634373	−	0.460899i
$790$	39.2517	+	63.1565i	1.39651	+	2.24701i
$791$	−1.88467	+	1.36929i	−0.0670112	+	0.0486865i
$792$	20.4323	+	6.63887i	0.726032	+	0.235902i
$793$		−	2.21013i		−	0.0784839i
$794$	−12.6022	+	38.7856i	−0.447236	+	1.37645i
$795$	6.06562	+	0.438946i	0.215125	+	0.0155678i
$796$	22.7910	+	70.1435i	0.807806	+	2.48617i
$797$	−29.5219	+	9.59224i	−1.04572	+	0.339775i	−0.780987	−	0.624547i	$-0.785284\pi$
$797$	−29.5219	+	9.59224i	−1.04572	+	0.339775i	−0.264732	+	0.964322i	$0.585284\pi$
$798$	0.0322369	−	0.0443703i	0.00114117	−	0.00157069i
$799$	30.1091			1.06518
$800$	−99.6467	+	17.0721i	−3.52304	+	0.603589i
$801$	−10.2180			−0.361035
$802$	−8.12353	+	11.1811i	−0.286852	+	0.394817i
$803$	5.49991	−	1.78703i	0.194088	−	0.0630629i
$804$	9.04941	+	27.8512i	0.319148	+	0.982237i
$805$	−1.80411	−	7.31143i	−0.0635864	−	0.257694i
$806$	−13.2707	+	40.8431i	−0.467441	+	1.43864i
$807$		−	7.87202i		−	0.277108i
$808$	−158.104	−	51.3712i	−5.56209	−	1.80723i
$809$	3.52799	−	2.56323i	0.124037	−	0.0901184i	−0.524037	−	0.851696i	$-0.675575\pi$
$809$	3.52799	−	2.56323i	0.124037	−	0.0901184i	0.648074	+	0.761577i	$0.275575\pi$
$810$	1.52469	−	21.0691i	0.0535722	−	0.740293i
$811$	3.16193	+	2.29728i	0.111030	+	0.0806683i	0.641915	−	0.766776i	$-0.278140\pi$
$811$	3.16193	+	2.29728i	0.111030	+	0.0806683i	−0.530885	+	0.847444i	$0.678140\pi$
$812$	−3.59179	−	4.94368i	−0.126047	−	0.173489i
$813$	−1.74380	−	2.40014i	−0.0611578	−	0.0841765i
$814$	−18.0283	−	13.0983i	−0.631892	−	0.459096i
$815$	2.05411	−	28.3849i	0.0719523	−	0.994280i
$816$	−63.9472	+	46.4604i	−2.23860	+	1.62644i
$817$	0.0706912	+	0.0229690i	0.00247317	+	0.000803582i
$818$		−	1.62251i		−	0.0567296i
$819$	−0.875235	+	2.69370i	−0.0305832	+	0.0941254i
$820$	2.95631	+	11.9809i	0.103239	+	0.418392i
$821$	−5.34837	−	16.4606i	−0.186659	−	0.574478i	0.813314	−	0.581825i	$-0.197661\pi$
$821$	−5.34837	−	16.4606i	−0.186659	−	0.574478i	−0.999973	+	0.00734722i	$0.997661\pi$
$822$	−18.3034	+	5.94714i	−0.638405	+	0.207430i
$823$	15.8575	−	21.8260i	0.552758	−	0.760806i	−0.437625	−	0.899157i	$-0.644180\pi$
$823$	15.8575	−	21.8260i	0.552758	−	0.760806i	0.990383	+	0.138351i	$0.0441803\pi$
$824$	114.478			3.98802
$825$	−0.585922	+	4.02711i	−0.0203992	+	0.140206i
$826$	−7.89561			−0.274724
$827$	17.8151	−	24.5204i	0.619492	−	0.852658i	−0.377823	−	0.925878i	$-0.623327\pi$
$827$	17.8151	−	24.5204i	0.619492	−	0.852658i	0.997316	+	0.0732195i	$0.0233274\pi$
$828$	−96.4742	+	31.3464i	−3.35271	+	1.08936i
$829$	−5.36074	−	16.4987i	−0.186186	−	0.573022i	0.813781	−	0.581172i	$-0.197406\pi$
$829$	−5.36074	−	16.4987i	−0.186186	−	0.573022i	−0.999967	+	0.00815004i	$0.997406\pi$
$830$	−93.3479	−	6.75523i	−3.24015	−	0.234478i
$831$	−2.38134	+	7.32901i	−0.0826078	+	0.254241i
$832$		−	76.9373i		−	2.66732i
$833$	44.3748	+	14.4182i	1.53749	+	0.499562i
$834$	10.1925	−	7.40525i	0.352936	−	0.256423i
$835$	−0.166464	−	0.267843i	−0.00576074	−	0.00926909i
$836$	−0.258528	−	0.187831i	−0.00894136	−	0.00649628i
$837$	13.9143	+	19.1514i	0.480950	+	0.661971i
$838$	−39.8265	−	54.8165i	−1.37578	−	1.89360i
$839$	−40.1585	−	29.1768i	−1.38642	−	1.00730i	−0.996247	−	0.0865571i	$-0.972413\pi$
$839$	−40.1585	−	29.1768i	−1.38642	−	1.00730i	−0.390178	−	0.920739i	$-0.627587\pi$
$840$	4.50428	−	5.34160i	0.155412	−	0.184303i
$841$	17.4861	−	12.7044i	0.602968	−	0.438082i
$842$	−85.5717	−	27.8039i	−2.94900	−	0.958187i
$843$		−	15.3365i		−	0.528217i
$844$	24.8966	−	76.6240i	0.856978	−	2.63751i
$845$	8.71113	−	5.41396i	0.299672	−	0.186246i
$846$	8.64474	+	26.6058i	0.297212	+	0.914725i
$847$	−0.397288	+	0.129087i	−0.0136510	+	0.00443547i
$848$	−27.9040	+	38.4066i	−0.958229	+	1.31889i
$849$	−25.1105			−0.861789
$850$	66.4901	+	64.8355i	2.28059	+	2.22384i
$851$	66.1221			2.26663
$852$	−33.4551	+	46.0470i	−1.14615	+	1.57754i
$853$	−2.71513	+	0.882198i	−0.0929642	+	0.0302059i	−0.355130	−	0.934817i	$-0.615563\pi$
$853$	−2.71513	+	0.882198i	−0.0929642	+	0.0302059i	0.262166	+	0.965023i	$0.415563\pi$
$854$	0.267253	+	0.822519i	0.00914520	+	0.0281460i
$855$	−0.116946	+	0.287440i	−0.00399946	+	0.00983025i
$856$	−14.1360	+	43.5062i	−0.483159	+	1.48701i
$857$		−	42.7681i		−	1.46093i	−0.682950	−	0.730465i	$-0.739304\pi$
$857$		−	42.7681i		−	1.46093i	0.682950	−	0.730465i	$-0.260696\pi$
$858$	−6.10045	−	1.98216i	−0.208266	−	0.0676697i
$859$	8.43776	−	6.13039i	0.287893	−	0.209166i	−0.434460	−	0.900691i	$-0.643061\pi$
$859$	8.43776	−	6.13039i	0.287893	−	0.209166i	0.722353	+	0.691525i	$0.243061\pi$
$860$	13.9576	+	5.67868i	0.475950	+	0.193641i
$861$	−0.282020	−	0.204899i	−0.00961120	−	0.00698295i
$862$	−15.9802	−	21.9948i	−0.544286	−	0.749146i
$863$	26.6537	+	36.6856i	0.907302	+	1.24879i	0.968080	+	0.250642i	$0.0806418\pi$
$863$	26.6537	+	36.6856i	0.907302	+	1.24879i	−0.0607782	+	0.998151i	$0.519358\pi$
$864$	−71.0637	−	51.6308i	−2.41764	−	1.75652i
$865$	37.8069	−	9.32891i	1.28547	−	0.317192i
$866$	8.81623	−	6.40537i	0.299588	−	0.217663i
$867$	23.0126	+	7.47725i	0.781549	+	0.253941i
$868$		−	12.2523i		−	0.415869i
$869$	−3.78211	+	11.6401i	−0.128299	+	0.394865i
$870$	−10.2738	−	8.66335i	−0.348316	−	0.293715i
$871$	5.99156	+	18.4401i	0.203016	+	0.624819i
$872$	64.4823	−	20.9516i	2.18365	−	0.709510i
$873$	25.9137	−	35.6671i	0.877044	−	1.20715i
$874$	1.30052			0.0439907
$875$	−4.02757	−	2.36459i	−0.136157	−	0.0799377i
$876$	−25.3344			−0.855969
$877$	−18.8505	+	25.9455i	−0.636538	+	0.876119i	−0.998425	−	0.0561029i	$-0.982133\pi$
$877$	−18.8505	+	25.9455i	−0.636538	+	0.876119i	0.361887	+	0.932222i	$0.382133\pi$
$878$	−69.2971	+	22.5160i	−2.33866	+	0.759878i
$879$	−3.38452	−	10.4165i	−0.114157	−	0.351339i
$880$	−24.2856	−	20.4787i	−0.818667	−	0.690336i
$881$	−7.14576	+	21.9924i	−0.240747	+	0.740942i	0.755560	+	0.655079i	$0.227365\pi$
$881$	−7.14576	+	21.9924i	−0.240747	+	0.740942i	−0.996307	+	0.0858631i	$0.972635\pi$
$882$			43.3512i			1.45971i
$883$	13.3603	+	4.34104i	0.449611	+	0.146088i	0.525066	−	0.851062i	$-0.324041\pi$
$883$	13.3603	+	4.34104i	0.449611	+	0.146088i	−0.0754544	+	0.997149i	$0.524041\pi$
$884$	−86.3419	+	62.7311i	−2.90399	+	2.10987i
$885$	−12.2915	+	3.03296i	−0.413176	+	0.101952i
$886$	63.3536	+	46.0291i	2.12841	+	1.54638i
$887$	−16.4400	−	22.6277i	−0.552002	−	0.759765i	0.438280	−	0.898838i	$-0.355588\pi$
$887$	−16.4400	−	22.6277i	−0.552002	−	0.759765i	−0.990282	+	0.139073i	$0.955588\pi$
$888$	36.0606	+	49.6332i	1.21011	+	1.66558i
$889$	3.40840	+	2.47635i	0.114314	+	0.0830541i
$890$	24.5997	+	10.0084i	0.824583	+	0.335483i
$891$	2.81287	−	2.04367i	0.0942346	−	0.0684655i
$892$	−64.0848	−	20.8224i	−2.14572	−	0.697186i
$893$		−	0.261495i		−	0.00875059i
$894$	2.82691	−	8.70032i	0.0945459	−	0.290982i
$895$	−1.52677	+	3.75265i	−0.0510344	+	0.125437i
$896$	4.08321	+	12.5668i	0.136410	+	0.419828i
$897$	18.1013	−	5.88148i	0.604386	−	0.196377i
$898$	−26.9386	+	37.0778i	−0.898953	+	1.23730i
$899$	−14.8093			−0.493917
$900$	−27.8522	+	56.4089i	−0.928408	+	1.88030i
$901$	22.8427			0.761001
$902$	−1.63747	+	2.25378i	−0.0545217	+	0.0750427i
$903$	−0.404833	+	0.131538i	−0.0134720	+	0.00437732i
$904$	−15.8384	−	48.7454i	−0.526776	−	1.62125i
$905$	−11.0742	+	6.88261i	−0.368119	+	0.228786i
$906$	4.51339	−	13.8908i	0.149947	−	0.461490i
$907$			11.8938i			0.394929i	0.980310	+	0.197464i	$0.0632706\pi$
$907$			11.8938i			0.394929i	−0.980310	+	0.197464i	$0.936729\pi$
$908$	31.6412	+	10.2808i	1.05005	+	0.341182i
$909$	−34.2066	+	24.8526i	−1.13456	+	0.824308i
$910$	4.74557	−	5.62775i	0.157314	−	0.186558i
$911$	16.3116	+	11.8511i	0.540427	+	0.392643i	0.824243	−	0.566236i	$-0.191601\pi$
$911$	16.3116	+	11.8511i	0.540427	+	0.392643i	−0.283817	+	0.958879i	$0.591601\pi$
$912$	0.403504	+	0.555375i	0.0133613	+	0.0183903i
$913$	−9.05459	−	12.4626i	−0.299663	−	0.412451i
$914$	48.6117	+	35.3185i	1.60793	+	1.16823i
$915$	0.732003	+	1.17780i	0.0241993	+	0.0389369i
$916$	51.1855	−	37.1884i	1.69121	−	1.22874i
$917$	−1.29689	−	0.421386i	−0.0428272	−	0.0139154i
$918$			80.6889i			2.66313i
$919$	6.05812	−	18.6450i	0.199839	−	0.615041i	−0.800047	−	0.599937i	$-0.795192\pi$
$919$	6.05812	−	18.6450i	0.199839	−	0.615041i	0.999886	−	0.0151038i	$-0.00480786\pi$
$920$	165.254	+	11.9588i	5.44826	+	0.394270i
$921$	−0.262331	−	0.807373i	−0.00864411	−	0.0266038i
$922$	−55.6325	+	18.0761i	−1.83216	+	0.595304i
$923$	−22.1504	+	30.4874i	−0.729090	+	1.00351i
$924$	1.83004			0.0602038
$925$	28.6291	−	29.3597i	0.941319	−	0.965342i
$926$	35.1478			1.15503
$927$	17.1141	−	23.5556i	0.562102	−	0.773667i
$928$	52.2620	−	16.9810i	1.71559	−	0.557427i
$929$	−0.548295	−	1.68748i	−0.0179890	−	0.0553644i	0.941659	−	0.336568i	$-0.109266\pi$
$929$	−0.548295	−	1.68748i	−0.0179890	−	0.0553644i	−0.959648	+	0.281204i	$0.909266\pi$
$930$	−6.45527	−	26.1610i	−0.211677	−	0.857854i
$931$	0.125221	−	0.385391i	0.00410395	−	0.0126307i
$932$		−	129.331i		−	4.23638i
$933$	11.5542	+	3.75419i	0.378268	+	0.122907i
$934$	35.0511	−	25.4661i	1.14691	−	0.833277i
$935$	−1.10327	+	15.2457i	−0.0360808	+	0.498586i
$936$	−50.4138	−	36.6278i	−1.64783	−	1.19722i
$937$	−16.0268	−	22.0590i	−0.523574	−	0.720638i	0.462560	−	0.886588i	$-0.346931\pi$
$937$	−16.0268	−	22.0590i	−0.523574	−	0.720638i	−0.986134	+	0.165950i	$0.946931\pi$
$938$	−4.45962	−	6.13815i	−0.145612	−	0.200418i
$939$	2.33621	+	1.69736i	0.0762393	+	0.0553911i
$940$	3.82629	−	52.8740i	0.124800	−	1.72456i
$941$	−27.8346	+	20.2230i	−0.907381	+	0.659251i	−0.940351	−	0.340206i	$-0.889503\pi$
$941$	−27.8346	+	20.2230i	−0.907381	+	0.659251i	0.0329704	+	0.999456i	$0.489503\pi$
$942$	9.45097	+	3.07081i	0.307929	+	0.100052i
$943$		−	8.26615i		−	0.269183i
$944$	30.5395	−	93.9910i	0.993977	−	3.05915i
$945$	−0.972130	−	3.93971i	−0.0316234	−	0.128159i
$946$	1.05120	+	3.23525i	0.0341774	+	0.105187i
$947$	53.3594	−	17.3375i	1.73395	−	0.563393i	0.739935	−	0.672678i	$-0.234856\pi$
$947$	53.3594	−	17.3375i	1.73395	−	0.563393i	0.994010	+	0.109285i	$0.0348560\pi$
$948$	31.5160	−	43.3781i	1.02359	−	1.40885i
$949$	−16.7737			−0.544498
$950$	0.563090	−	0.577460i	0.0182690	−	0.0187353i
$951$	19.0779			0.618644
$952$	15.4263	−	21.2325i	0.499969	−	0.688148i
$953$	14.6164	−	4.74916i	0.473472	−	0.153840i	−0.0625545	−	0.998042i	$-0.519925\pi$
$953$	14.6164	−	4.74916i	0.473472	−	0.153840i	0.536026	+	0.844201i	$0.319925\pi$
$954$	6.55845	+	20.1848i	0.212338	+	0.653508i
$955$	18.0443	+	1.30580i	0.583900	+	0.0422547i
$956$	12.4751	−	38.3943i	0.403472	−	1.24176i
$957$		−	2.21196i		−	0.0715025i
$958$	49.1701	+	15.9763i	1.58861	+	0.516171i
$959$	2.94108	−	2.13682i	0.0949725	−	0.0690016i
$960$	25.4819	+	41.0007i	0.822425	+	1.32329i
$961$	1.05721	+	0.768107i	0.0341035	+	0.0247776i
$962$	37.9923	+	52.2919i	1.22492	+	1.68596i
$963$	6.83878	+	9.41277i	0.220377	+	0.303322i
$964$	−103.932	−	75.5107i	−3.34741	−	2.43203i
$965$	−38.3901	+	45.5267i	−1.23582	+	1.46556i
$966$	−6.02538	+	4.37770i	−0.193863	+	0.140850i
$967$	24.2627	+	7.88342i	0.780234	+	0.253514i	0.671940	−	0.740605i	$-0.265461\pi$
$967$	24.2627	+	7.88342i	0.780234	+	0.253514i	0.108294	+	0.994119i	$0.465461\pi$
$968$		−	9.19070i		−	0.295400i
$969$	0.102073	−	0.314148i	0.00327905	−	0.0100919i
$970$	−97.3223	+	60.4858i	−3.12483	+	1.94208i
$971$	−2.83589	−	8.72796i	−0.0910079	−	0.280094i	0.895185	−	0.445695i	$-0.147043\pi$
$971$	−2.83589	−	8.72796i	−0.0910079	−	0.280094i	−0.986193	+	0.165602i	$0.947043\pi$
$972$	−81.2025	+	26.3843i	−2.60457	+	0.846277i
$973$	−1.39882	+	1.92532i	−0.0448442	+	0.0617228i
$974$	112.133			3.59297
$975$	5.22589	−	10.5839i	0.167362	−	0.338958i
$976$	−10.8251			−0.346504
$977$	−20.5442	+	28.2767i	−0.657267	+	0.904651i	−0.999387	−	0.0350056i	$-0.988855\pi$
$977$	−20.5442	+	28.2767i	−0.657267	+	0.904651i	0.342120	+	0.939656i	$0.388855\pi$
$978$	−26.7682	+	8.69750i	−0.855951	+	0.278115i
$979$	1.35078	+	4.15727i	0.0431711	+	0.132867i
$980$	30.9587	−	76.0933i	0.988941	−	2.43071i
$981$	5.32883	−	16.4004i	0.170136	−	0.523626i
$982$			39.2001i			1.25093i
$983$	−20.0925	−	6.52844i	−0.640850	−	0.208225i	−0.0294746	−	0.999566i	$-0.509383\pi$
$983$	−20.0925	−	6.52844i	−0.640850	−	0.208225i	−0.611375	+	0.791341i	$0.709383\pi$
$984$	6.20481	−	4.50806i	0.197802	−	0.143712i
$985$	17.4392	+	7.09516i	0.555658	+	0.226071i
$986$	−40.8377	−	29.6703i	−1.30054	−	0.944896i
$987$	0.880222	+	1.21152i	0.0280178	+	0.0385632i
$988$	0.544813	+	0.749871i	0.0173328	+	0.0238566i
$989$	−8.16599	−	5.93294i	−0.259663	−	0.188656i
$990$	−13.7885	+	3.40234i	−0.438228	+	0.108133i
$991$	−26.7798	+	19.4567i	−0.850690	+	0.618062i	−0.925336	−	0.379148i	$-0.876217\pi$
$991$	−26.7798	+	19.4567i	−0.850690	+	0.618062i	0.0746463	+	0.997210i	$0.476217\pi$
$992$	104.788	+	34.0476i	3.32701	+	1.08101i
$993$			10.5591i			0.335084i
$994$	4.55688	−	14.0246i	0.144536	−	0.444835i
$995$	−23.4231	−	19.7514i	−0.742563	−	0.626162i
$996$	20.8542	+	64.1826i	0.660790	+	2.03370i
$997$	8.80167	−	2.85984i	0.278752	−	0.0905719i	−0.166305	−	0.986074i	$-0.553184\pi$
$997$	8.80167	−	2.85984i	0.278752	−	0.0905719i	0.445057	+	0.895502i	$0.353184\pi$
$998$	−40.8597	+	56.2386i	−1.29339	+	1.78020i
$999$	35.6294			1.12727

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	275.2.y.b.34.14	✓	56
25.8	odd	20		6875.2.a.n.1.55		56
25.14	even	10	inner	275.2.y.b.89.14	yes	56
25.17	odd	20		6875.2.a.n.1.2		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
275.2.y.b.34.14	✓	56	1.1	even	1	trivial
275.2.y.b.89.14	yes	56	25.14	even	10	inner
6875.2.a.n.1.2		56	25.17	odd	20
6875.2.a.n.1.55		56	25.8	odd	20

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	275.y (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.59706 - 2.19817i) q^{2} +(0.774067 - 0.251509i) q^{3} +(-1.66330 - 5.11912i) q^{4} +(1.70943 + 1.44147i) q^{5} +(0.683373 - 2.10321i) q^{6} +0.417733i q^{7} +(-8.74087 - 2.84008i) q^{8} +(-1.89113 + 1.37399i) q^{9} +(5.89867 - 1.45551i) q^{10} +(0.809017 + 0.587785i) q^{11} +(-2.57501 - 3.54420i) q^{12} +(-1.70490 - 2.34659i) q^{13} +(0.918248 + 0.667146i) q^{14} +(1.68576 + 0.685855i) q^{15} +(-11.4935 + 8.35055i) q^{16} +(6.50132 + 2.11241i) q^{17} +6.35136i q^{18} +(0.0183461 - 0.0564634i) q^{19} +(4.53575 - 11.1484i) q^{20} +(0.105064 + 0.323353i) q^{21} +(2.58410 - 0.839626i) q^{22} +(-4.73883 + 6.52244i) q^{23} -7.48033 q^{24} +(0.844328 + 4.92820i) q^{25} -7.88104 q^{26} +(-2.55349 + 3.51457i) q^{27} +(2.13842 - 0.694816i) q^{28} +(-0.839822 - 2.58471i) q^{29} +(4.19989 - 2.61023i) q^{30} +(1.68388 - 5.18245i) q^{31} +20.2197i q^{32} +(0.774067 + 0.251509i) q^{33} +(15.0265 - 10.9174i) q^{34} +(-0.602150 + 0.714087i) q^{35} +(10.1791 + 7.39556i) q^{36} +(-4.82073 - 6.63516i) q^{37} +(-0.0948162 - 0.130503i) q^{38} +(-1.90990 - 1.38762i) q^{39} +(-10.8481 - 17.4546i) q^{40} +(-0.829485 + 0.602656i) q^{41} +(0.878579 + 0.285468i) q^{42} +1.25198i q^{43} +(1.66330 - 5.11912i) q^{44} +(-5.21332 - 0.377268i) q^{45} +(6.76921 + 20.8335i) q^{46} +(4.18899 - 1.36108i) q^{47} +(-6.79653 + 9.35462i) q^{48} +6.82550 q^{49} +(12.1815 + 6.01466i) q^{50} +5.56375 q^{51} +(-9.17672 + 12.6307i) q^{52} +(3.17803 - 1.03261i) q^{53} +(3.64755 + 11.2260i) q^{54} +(0.535686 + 2.17095i) q^{55} +(1.18640 - 3.65135i) q^{56} -0.0483206i q^{57} +(-7.02287 - 2.28187i) q^{58} +(-5.62783 + 4.08886i) q^{59} +(0.707046 - 9.77038i) q^{60} +(0.616446 + 0.447874i) q^{61} +(-8.70263 - 11.9781i) q^{62} +(-0.573959 - 0.789987i) q^{63} +(21.4593 + 15.5911i) q^{64} +(0.468130 - 6.46890i) q^{65} +(1.78909 - 1.29985i) q^{66} +(-6.35746 - 2.06566i) q^{67} -36.7946i q^{68} +(-2.02772 + 6.24067i) q^{69} +(0.608013 + 2.46407i) q^{70} +(-4.01481 - 12.3563i) q^{71} +(20.4323 - 6.63887i) q^{72} +(3.39913 - 4.67850i) q^{73} -22.2842 q^{74} +(1.89305 + 3.60240i) q^{75} -0.319558 q^{76} +(-0.245537 + 0.337953i) q^{77} +(-6.10045 + 1.98216i) q^{78} +(3.78211 + 11.6401i) q^{79} +(-31.6845 - 2.29289i) q^{80} +(1.07442 - 3.30672i) q^{81} +2.78583i q^{82} +(-14.6506 - 4.76028i) q^{83} +(1.48053 - 1.07567i) q^{84} +(8.06861 + 12.9825i) q^{85} +(2.75207 + 1.99950i) q^{86} +(-1.30016 - 1.78951i) q^{87} +(-5.40216 - 7.43543i) q^{88} +(3.53639 + 2.56934i) q^{89} +(-9.15530 + 10.8572i) q^{90} +(0.980249 - 0.712193i) q^{91} +(41.2712 + 13.4098i) q^{92} -4.43507i q^{93} +(3.69818 - 11.3818i) q^{94} +(0.112752 - 0.0700751i) q^{95} +(5.08545 + 15.6514i) q^{96} +(-17.9371 + 5.82813i) q^{97} +(10.9008 - 15.0036i) q^{98} -2.33756 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 16 q^{4} - 7 q^{5} - 4 q^{6} - 15 q^{8} + 10 q^{9} + 10 q^{10} + 14 q^{11} - 20 q^{12} - 6 q^{14} - 21 q^{15} - 20 q^{16} + 20 q^{17} + 10 q^{19} + 22 q^{20} - 6 q^{21} + 10 q^{23} - 62 q^{24} + 9 q^{25}+ \cdots + 70 q^{99}+O(q^{100}) \) 56 * q + 16 * q^4 - 7 * q^5 - 4 * q^6 - 15 * q^8 + 10 * q^9 + 10 * q^10 + 14 * q^11 - 20 * q^12 - 6 * q^14 - 21 * q^15 - 20 * q^16 + 20 * q^17 + 10 * q^19 + 22 * q^20 - 6 * q^21 + 10 * q^23 - 62 * q^24 + 9 * q^25 - 4 * q^26 + 18 * q^29 - 129 * q^30 - 16 * q^34 + 42 * q^35 - 26 * q^36 - 65 * q^37 - 20 * q^38 + 20 * q^39 - 28 * q^40 - 10 * q^41 + 60 * q^42 - 16 * q^44 - 18 * q^45 + 6 * q^46 - 25 * q^47 + 15 * q^48 - 104 * q^49 + 98 * q^50 + 54 * q^51 + 90 * q^52 + 5 * q^53 + 55 * q^54 - 3 * q^55 + 10 * q^56 - 10 * q^58 + 34 * q^59 + 133 * q^60 - 20 * q^61 - 10 * q^62 + 20 * q^63 + 25 * q^64 - 10 * q^65 + 4 * q^66 - 15 * q^67 - 2 * q^69 - 4 * q^70 - 13 * q^71 - 5 * q^72 - 70 * q^73 - 30 * q^74 - 80 * q^75 + 140 * q^76 - 65 * q^78 + 15 * q^79 - 131 * q^80 - 99 * q^81 + 60 * q^83 + 76 * q^84 + 43 * q^85 + 43 * q^86 - 175 * q^87 + 30 * q^88 + 27 * q^89 + 73 * q^90 - 10 * q^91 - 80 * q^92 - 17 * q^94 + 18 * q^95 - 148 * q^96 - 15 * q^97 - 80 * q^98 + 70 * q^99

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